So I am about 3-4 days late for my period and I have been having sharp pains around where my left ovary is. Could this mean that I'm pregnant?

Absolutely not...

You can't possibly feel being pregnant for months... much less 3 days. Its something else causeing it...

And at 3 days you can't even test to find out if you are pregnant yet... thats assuming you actually even are...

You have to be 2 WEEKS late to take a HPT... when you might get a result you can start to trust... and 4 weeks late before you can get a result you can be confident of. (false negatives are rare after 4 weeks when taken correctly)