Having sharp pains in on my right side and lower back hurts could that be a sign of pregnancy?

Yes and other possib: If these symptoms are severe or progressing, or you are feeling sick like with a fever or vomiting, then you should get checked right away. There are just too many bad things that could cause this, including pregnancy and life threatening conditions

Yes: Yes, it's possible. If you are worried you should go ahead and get a pregnancy test.