My boyfriend ejaculated in me June 17 or 18 which is when my period was ending. Yesterday I took a test and it came out negative. Today when I woke up I felt like there was no energy and I felt so tired and helpless. I ate and an hour later I threw up so much. Could I be pregnant?

Any time you have sex pregnancy is possible. So yes, you could be pregnant.

How late is your period?

Edit: Just re-read your question. You had sex 13 days ago? It's too early to test, and too early for symptoms. You'll have to wait and see what happens with your next period. If you miss it wait 2 weeks, then test using first morning urine. Any test you take right now will likely be negative because it's too early to test.

Yes you could be pregnant. But it's way too soon to know and you are probably stressing yourself out worrying about it.