My Best friend had recently broken up with her boyfriend. During the time she was struggling with her relationship, I helped dealing with lots of stress. She had decided to move to another state. Ever since she got back, I feel different about our friendship. First she has not answer my phone calls, and when she answers, she tells me she has to go out. Is she trying to avoid me?

Sounds like she is trying to avoid you
Question is WHY?

Maybe she feels that she isn't ready to deal with anything because she isn't over him enough yet

Maybe she is concerned that you may want more than a friendship and she isn't ready or wanting that

Let her know that you are still there for her anytime she wants a friend to talk to. Not much more you can do until she comes around.

There's an old saying "You can never go back home again." I'm sure this is exactly what your friend is experiencing, having moved away and then returned, not to mention dealing with the recent breakup and everything. She's got a lot on her plate right now. Give her some time to adjust ; I don't think your friendship is over.

Your friend is politely taking time for herself. Let her.

She is avoiding you, but it doesn't mean there's something wrong with you. Just give her time and space to deal with her issues. When she's ready and if she wants to talk to you, she will find a way to contact you. Just let her be for now.