Regarding whether or not you are in the wrong for wanting to be able to intellectually back up your faith. The answer is a very emphatic NO. Before I go any further with that thought, let me share some scriptures with you: Isaiah 1:18, Peter 3:15, Jude 1:3.
The Bible is very clear that seeking to know the ways of God which correspond to our intellect is not wrong. I believe with all my heart that God through time has revealed to us the tools of science to allow us to explore and understand this world he created. The intellect is not to be abandoned in the quest for meaning, purpose, and the supernatural. In fact, how desperately we need our intellect and our rational minds in order to have discernment in these perilous and deceiving times. There are so many lies being perverted on the church of Christ today and so many people who are buying into them, that people like you and I need to be ready,willing, and able to answer the toughest questions thrown at us. I don't see this need for intellectual confirmation as a place of doubt, but rather a place of faith! You told me yourself that while you seek answers to these questions, you still do not doubt the Bible as God's inerrant word or that Jesus Christ is Lord. You have experienced these things for yourself, you simply want to be able to take what you have existentially experienced and transfer it into a coherent worldview. Your faith is well intact and I applaud you for taking the pursuit of knowledge so seriously.
Recently one of my youth group kids went to a mens conference called "Iron Sharpen Iron". I was not able to go but I was so pleased to see Him going to grow as a young christian male. But it was not long before I started receiving frantic text messages from him. Apparently the men had seperated into groups of several hundred, but within this kids group was apparently someone who seemed to be an atheist. As soon as discussion got underway, this atheist was up front and center presenting challenges to the Christian faith and the Bible. He was apparently very viscous and vociferous. But the reason that I was getting such frantic texts was that out of several hundred men in this auditorium, not ONE of them could say ANYTHING in response to this atheist. He was completely decimating anyone who tried to stand up to him and no one was prepared to challenge these lies! The texts continued, asking me for advice on this subject or the next in the hopes that someone could refute this atheist. I was so mad at this point for two reasons: 1. This atheist was winning this debate and shaming the name of God, and 2. that out of several hundred grown men, many of whom lead youth groups, not one could stand to give an apologetic defense.
However, it turned out for the best. Apparently, this "atheist" was actually a Christian apologist who was playing the "other side" role in order to challenge these men and show them how unequipped they really were. When I heard that I started praising God for people like that who are willing to go out and WAKE THE PEOPLE UP! We live in a world full of lies, deception, and false philosophy. We live surrounded by people who have somehow squeezed into their own lives contradicting philosophies and they are blind to their own spiritual destitution. We live in a world full of pseudo-intellectuals who are fully able and prepared to block any theistic talk in the realm of science. We need to have our minds purified and our hearts ready for war for the kingdom of Christ. We need to reason, contend, and proclaim with all humility and boldness.
I just want to quickly make one distinction between doubt, questions, and unbelief. Questions are where you still believe the basic premise, but you seek to clarify the position to better defend it and bring it coherence. Doubt is when you question the premise on the assumption that it is wrong with and intent to prove it right. And unbelief is when you refuse to obey the commands or believe the premise. So to put it simply..
Questions: True until proven false
Doubt: False until proven true
Unbelief: Always false, never true.
I will go so far as to say that the first two do not concern me nearly as much as the last. I don't believe that testing your beliefs and asking questions to be confident and equipped is a sin or it is wrong. As you can see in the scripture I posted, God is more than willing to reason with us and he encourages us to be prepared to defend the faith. How else do we learn to defend the faith if we do not spend much time asking questions, learning, and going through the thinking of our day? But doubt, doubt is an entirely different animal. Doubt is when one little contradiction pops up in my mind and it throws my whole world into upheaval. Doubt is when my lack of understanding leads me to lose confidence in the God I place my faith in. Let me give you an example of this in Matthew 14:22-33.
I want to focus here on Peter and show both an awesome example of faith and doubt in the same passage. Try to imagine that you are a poor, uneducated fisherman living in those days. How would you feel if you saw someone walking on the water towards you? I don't blame them at all for thinking it was a ghost, how could they know any better? But Jesus, tender and loving as he was, calls out to them to not fear. Now, right here in verse 28 we see the awesome faith of Peter. Notice the "getting out of the boat" was not the idea of Jesus, but rather Peter. Peter so desperately wanted to be near His Lord that he opted to go walking on the water too. Notice his faith that not only gave him the notion that he too could walk on the water, but the faith to then GET OUT of the boat. Faith is a verb, and Peter just proved it. But even upon witnessing this miracle and walking across the water, Peter still lost focus of the truth and allowed himself to be intimidated by the surroundings. The crashing waves and the high winds that normally would strike fear of death into fisherman were starting to take their toll as Peter walked towards Jesus. And as he took his eyes off the Lord, doubting that he would be safe, he began to sink. And if you and I take our eyes off of Jesus, we will begin to sink too. It feels that way dosent it? Even in the trials of our mind and our soul, when we lose heart and doubt the Lord...it feels like our life begins to sink back into the world and into despair. And it never ceases to amaze me. God has shown me His favor and His hand so many times in my life, and yet challenges sometimes still cause me to doubt as if God needed to prove Himself AGAIN or I would not believe Him. Finally, and quickly, unbelief is just a refusal to put our weight on the promises of God. This is a state of the heart, not the mind. I don't think I need say any further because this applies to neither of us.
So, in conclusion, make sure you draw the line between educating yourself and doubting the Lord. Someone said it to you well when they said that the faith comes first, then the evidence. God responds with confirmation only to our faith. Apologetics is great, but all it really does in the end is knock down the barriers people erect to stop themselves from having to put their faith in God. You will never argue someone into the kingdom of God. God still requires us to walk by faith, not by sight. And conversion is still a work of the Holy Spirit.