I'm a Christian just FYI...
I think it's very reasonable to question the nature of EVERYTHING. However, most things we believe, ultimately, cannot be proved and therefore we all need to act upon the limited evidence we've been given. I think if God gives you no sign of his existence, then it's not fair for you to be condemned for not following him...However, I believe it's our duty as humans to examine our lives and live virtuously and defining that is hard without seeking out truth wherever it may be found. (Which in my experience leads back to God)
I wish you luck on your journey...if you're still conflicted at all or want to hear more logical defenses of Christianity, I'd recommend reading "Mere Christianity" and "The Great Divorce" by C.S. Lewis.
This. ^
The way you feel is normal. Every Christian has periods of doubt and times when they don't feel close to God. I think organized religion is the problem. It fails us as humans. It sets a lot of rules and ideals for you to follow and there's the whole building full of people watching to see if you do or not.
When I was a little older than you (almost 20 years ago), I went through a period when I questioned everything I'd been taught. I had to find a way to reconcile what was happening in my life with my faith. There was a time when I'd almost completely turned my back on God and He reached out to me.
Needless to say, the doubts have been gone since, but I don't attend church anymore. In the process, I lost pretty much my entire friend base. Think it through. Process your thoughts fully. Prepare for a disconnect, but know that you can recover. I wish you the best on your journey.