Your best option is return to your own university after your suspension. Then do not do anything that could be considered cheating, and you will have a clean record when you apply to grad school. Do not try to transfer now. The suspension will appear on your records, and it is not likely that any college or university (other than an open admission community college) will accept you.
Did your friend confess that he copied your work, or is the problem that the university thinks that you may have copied his? Were you both suspended?