After I have an abortion is it necessary to see my doctor? And if so, what will the doctor be doing?

For one make sure you don't develop sepsis... an infection that could kill you. So spend the money, go to the doctor. Its for your own health.

Yes, you should see your doctor after an abortion. He/she will be checking to make sure the bleeding stops, to make sure everything was removed, and more. It's important to have follow up appointments after an abortion, just like it would be after giving birth.