Can you get pregnant on the first day of your period?

Okay bit of a story but I'm in desperate need of advice. August 20 me and my significant other were having sex and on the withdrawal, I saw that I had started my period. (Cringe) I hurry to the shower to get cleaned up. Then insert my Diva cup, lovely alternative to tampons. All seems well. After I leave the bathroom my boyfriend tells me it was a "close one" but I brush this off, he says this often. When I emptied the cup though there was this clear stringy mucus looking clot like thing that was in it with a good amount of blood. I again brush it off as just discharge. It's now September 15th and I'm feeling dizzy all the time kind gross feeling when I wake up, but no vomiting. Also I work at a burger joint and I can't stand the smell of the hotdogs we have. Never had this problem before, but last week the smell drove me off line. Not to mention I'm pretty sure my nipples are changing shape, it's so minute it's hard to tell. Does anyone have any advice?