(Potentially) Low GPA with No Reserach Experience, Am I Screwed for math PhD program?
I can't speak for math specifically but here is a general answer

First, don't worry about no research experience. some US undergraduates have research experience but not all. I had literally zero and I was admitted to very prestigious universities

As to GPA, there's nothing you can do about the past grades so just do the best you can on remaining classes. You can mention something about it in your cover letter if you want (ie some explanation like in your question). 3.5 is not the worst GPA in the world. 

GRE scores matter more or less at different places. Just study the best you can.

You can also make sure your research statement is well written. Find universities where there are professors whose interests match yours very well

In short I don't think you're in a hopeless situation.