No HIV is not curable.
Keep all follow up questions to 1 thread.
It might be a good idea for you to consult the "Hiv anxiety" support group as you are struggling with a fear of HIV and all you are required to do is to find a clinic that will test you for free if you can't afford the test.
As you were told, there is no cure available for HIV. However development of ARV medication has reduced the death rate very significantly and therefore HIV is no more a death sentence in the developed world.
HIV treatment is available but not cure, which, despite their side effects, helps the HIV patients having normal life through controlling their viral load.
If anyone claims for HIV cure, he is lying. At the moment, care is the only cure for HIV