Hi all, would really love some options as I'm pretty stumped

I'm currently on birth control and have skipped 6 consecutive periods up until last week.
Last week Monday and Tuesday I had unprotected sex, I didn't take birth control on either of those days, I did on Wednesday but didn't on Thursday and have continued not to incase I conceived.

I had brown discharge from last Monday, and on the Friday pink /red blood also that I'm still experiencing now, so 3 days of fresh blood

My question is, is it possible to have fallen pregnant but experience a withdrawal bleed from all the pills I've missed?
I'm experiencing lightheadedness, nausea and have vomited twice.
It's 7 days today since unprotected sex and expectedly the hpt is negative as it's too early to test.
Planning on going to the gp this week as I'm really not feeling well.
Has anyone else experienced something similar?