I slept with my partner Wednesday night after having my period end on the 21st of October. I am not on any form of contraception. Now today I am experiencing cramps in my lower abdomen, bloating, and I bled a little. Ive felt slightly dizzy and nauseous in the mornings and threw up the morning after I had sex. Could I be pregnant?

Yes you could, but far to early to have any significant symptoms.

ANY time there is penile insertion there is the risk of pregnancy. So yes it is possible you are pregnant. But, as Ben said it is too early for any symptoms to manifest themselves. So whatever you are feeling its not due to being pregnant.