There's a lot of people out there who feel they were born into the 'wrong' body - one of my friends is a pre-op transexual, male-to-female, but I've also known someone in the past who was female-to-male.
I don't think it means that God made a mistake, sometimes a lot of things happen for a reason and we just don't understand why at the time.
If you think you might be transgender you really need to get advice from the professionals, find out exactly what's involved and whether it's going to be the right thing for you.
In all the cases that I've known about people have had to go for extensive psychological assessment, counselling and drug treatment before surgery is even considered, so just making enquiries at this stage is not going to commit you to anything irreversible! It'll just give you a chance to find out what your choices are.
It sounds like you're also going to need good spiritual advice/support from people who won't judge you or try to tell you what they think is best for you - I know when it comes to religion everyone thinks they know best, but true faith really is about finding your own way through life, irrespective of what other people are doing or thinking. As long as you're not hurting anyone else, who's got the right to judge you?
Good luck.

I don't think God makes mistakes. I don't know why some of us have genetic problems to deal with. But then God doesn't promise us a trouble free life, just that he will walk beside us when troubles come. I don't know if you are a transexual or not, but with your concerns, I think you should definately seek counseling. If you and your consellor decide a sex change is in order, then I don't really see a conflict with faith in God. I have NF, which means my body grows many tumors. I don't have any conflict with my faith when I have one removed. I don't see a sex change as any different. I don't know what lies ahead for you, but I do believe if you call on God, he will stand with you all the way. God bless you.