I got my first depo shot a few months ago,
It messed with my period a little bit but it never went away.
3 months later I was due for my next shot.. but I didn't get it until about a month & half until I was supposed to.
#1) if you are late for your depo shot, and having un protected sex,what are the chances of getting pregnant?
..
While I was late for the next shot.. I got my period. A few days after I got my period I had un protected sex several times in the following week.

About 3 weeks after I had unprotected sex I went to the doctor to get my missed depo shot, they gave me a pregnancy test and it came up negative.
I should have gotten my period about 2 or 3 weeks ago, but it never came..

#2) Did I miss my period from pregnancy or miss it because the 2nd depo shot?

I've been feeling a little sick to my stomach. Dry heaving. I've been getting headaches. And I've been peeing like every hour.
Should I take a pregnancy test? Please help.

Try a pregnancy test.

Pregnancy on Depo can happen. No form of birth control is 100% effective even when used correctly, and you definitely didn't use it correctly, so the odds do increase.

Try a home pregnancy test. Use first morning urine for more accuracy.