Are you aiming for retail/commercial banking or IBD/markets? They have pretty different expectations for interns/grads

For retail/cmb I think you are good to go, check out those MT/summer intern profiles on linkedin, sometimes they dont really have banking experience

For IBD/markets its a stretch. You probably would not be able to score a BB summer internship with your current profile. You can look for part time/semester internships/placements for relevant firm/teams(valuation/M&A/asset management) and make moves from there.