Do I still have a shot - 3.8GPA

IDK but quadruple posting doesn't help the cause

I was at an almost identical position as you are at a slightly better ranked school than Georgetown (U.S. News & World Report better I mean, obviously the differences can be minute and it's silly to say that one school is simply "better" than another at the top 20 or so). Similar GPA, no internship, etc. My advice: see if your career center has an externship program. Use your alumni network (there literally should be a website), advance search the city you want to work in, search which firms you want, and start cold-emailing people to introduce yourself, ask if they'd be willing to talk to you over the phone, ask them for advice, ask them if you can come shadow for a day, etc. Believe me, you will earn their respect and you'll most likely get them to refer you to HR to put you in a good category when the final round interviews come around in the fall. Whatever you do this summer, try to find some sort of externship, shadowing opp, or something, within finance/banking/S&T/whatever you want to do. It shouldn't be that hard to do something that even lasts for a few days, put it on your resume, and use it going forward for the fall. This is what I did and I ended up with a FT BB front office opportunity that I was shooting for the entire time.