Choosing design can be a tough road, but the journey is worth it in my opinion. If this is the work you enjoy doing I’d relax a little bit, and instead focus on doing the best work you possibly can. Everything else will hinge off of that. Connections are useless without the abilities to appeal to them. At least to me. I get portfolios from friend’s of co-workers kids all the time. If the portfolio stinks it is straight into the trash.
So, work on your core skills. Instead of worrying about not being able to sketch, correct the problem and work at it for at least 2 hours every day. By then end of the semester you will be great. Start a discussion in the sketch forum and post in it EVERYDAY. If you are dedicated to improving, you will do it. If you are not dedicated you reduce your odds in being able to make it. The answers lie within you, you just have to pony up to do the work.
I never really had a great internship, it took me 6 months to find a job after school, but I didn’t just sit around watching cartoons waiting for the phone to ring. I reworked a project in my portfolio every week Monday through Thursday. Fridays I would make new portfolios and send them out. Eventually I landed a job. 20 years later I’m a CDO at a decent sized company with an interdisciplinary team of designers. If I had given up in those first 6 months after school it would have all been wasted.
As far as your diverse background, in time this will be come an asset. A lot of firms like IDEO and Frog specifically look for people like you.
I’ll leave you with one last question. Would you rather fail doing what you love or be successful doing what you know you will hate? The answer to that question determines a lot of things.