Replacing Hacked Phone

Hi there, 
I have an old Galaxy A8 that I am using with my AT&T prepaid plan. About a month ago I was informed that one of my phone contacts info (stored only in my phone) was sent in messages from my instagram account to several of my friends. I switched to two factor and changed my passwords on everything I could, but my phone still isn't running quite right and I'd like to replace it. 

My question is whether I can use my existing sim card in my new phone, or if that poses a risk? I am concerned about it because the phone number sent via instagram messages would only be found among my phone contacts, I don't have it elsewhere. If I need a new sim card how do I go about getting one, and what is the easiest way to move my contacts etc?

Thanks! -m