When a person does a blood test does the doctor test to see if that person have AIDS too.

Yes, if you ask them to.

In routine labwork (like at a check-up, where the doctor checks your cholesterol and CBC, etc) an HIV test is not included. In fact, a doctor cannot (or is not supposed to by law) order an HIV without having the patient sign a consent form first. So, the answer is no. I am a med tech and work in a lab and run the tests you are speaking of so you can trust my answer is correct.