I am 20. I had a period on the 28th of July going into August. I haven't had a period since, and have been dizzy, nauseous, tired, have sore breast, and diarrhea. One night I only took one shot of vodka and the next day I had a terrible hangover, and ciggaretts (which I have been smoking since I was 14) are making me gag and even vomit. Could I be pregnant?

If you engaged in sex then yes you could be pregnant. Take a HPT using first morning urine.

You say your last period was the week going into August,that's only 2 weeks ago so another period wouldn't be due yet for a further 2 weeks.It's possible that yes you could be pregnant,although it is very early on at the moment.
I'm not sure if a pregnancy test would be 100% at 2 weeks,although I'm sure there are some on the market that will state that they do.
Perhaps it may be best to wait just 2 weeks more to see if you miss the next period,if so then visit your Doctor who will be able to confirm it for sure.