This is a forum mainly for questions about R, not a stats advice forum.
If it is at all possible you need to consult with a statistician one--on--one. They can discuss what the research questions are, any assumptions you are making and so on and possibly do some basic exploratory analysis.
In a pinch, you are probably much better off asking for advice on https://stats.stackexchange.com/ which is a stats advice forum.
Probably there are any number of things that are better than t-tests but it is hard to say what without a lot more information.