A couple of months ago, I had blood work done for normal things (cholesterol, lipids, the whole chabang). The doctors said that my bloodwork was fine. Now, if I had HIV, would thwy have been able to see it even though it wasn't on the prescription to be tested for? By them saying that my blood was fine, does that mean that there were absolutely no problems with the blood or is there a possibility of HIV not being seen?
Blood Test Question
If they didn't test for HIV then they can't tell. Only if the infection is causing some secondary problems, then they might tell that something was wrong.
During a full-spectrum test (as it seems you are describing) they would do a CD4 count (basically, your immune system) if there was an abnormally low amount of them, they would move on to a more appropriate and accurate test.