Hello!

The first day of my last period was May 8th, but it was only 3 days long when it's usually 5 to 7 days. I missed 4 days of my pill (which is fine because my fiancé and I would like to get pregnant but don't want to force it). My ovulation day was May 17th according to my Ovia app and yesterday, May 19th, I started bleeding. Today, May 20th, I'm still bleeding, heavy enough to fill a tampon half way. I have cramps, headache and nausea. On my normal period I only have cramps. Am I pregnant this early?

No, it does not sound like pregnancy, sound like issues of missing pills perhaps.

Also ovulation apps are nice for fun, and guessing, but are often wrong. If you really plan on pregnancy, you will need to test and track ovulation