I started my last period on the 9/3 and finished on the 12/3. I had unprotected sex on the 16/3. My next period is roughly meant to start on 8/4.
I've been very bloated, cramping and have been hungry but can't decide what I what to eat, is there a chance that I'm pregnant?

Any time you have unprotected sex, you could get pregnant.

Yes, there's a chance that you're pregnant.

You'll have to wait for your period, if you miss it wait 2 weeks then test using first morning urine. Any time you have sex, even with protection, pregnancy is possible. If you're having unprotected sex I'm assuming you're trying to conceive, so good luck, and baby dust your way.