If you miss three pills, your hormone level are going to go a little crazy. So what you described sounds normal to me. If you still want to prevent pregnancy, you might want to use a backup method since you missed so many pills.

Is it possible for me to end up pregnant now even though I'm bleeding?

Anything is possible. Women can get pregnant if they take the pill perfectly, and women can get pregnant even if they are right in the middle of their period.

.since you missed three pills in a row you do have an increased risk of pregnancy, but since you are bleeding it is hard to tell. .if you are worried about it take a test in about two weeks to be sure.