If both of your parents are O then you're O. If one is A and one is B then you're AB. If mother is A and father is O then you should be A and O if the other way around. If mother is B and father is O then you should be B and O if the other way around.
There is no way you can tell your blood type without a test, be it at your doctor's or a home kit. If you know your parents' types, then you can narrow it down, but you still need a blood test to ascertain which one it is. Talk to a doctor about this.