You correctly identified the three risks for HIV, which means that your event was NOT a risk for HIV. Forget about it and move on.
Honestly you shouldn’t even worry . The risk is very very low. Hep B & Hep C can be transmitted like that, but the risk is almost nonexistent . If it’s really wearing you down, make an appointment with a doctor and get the Hep vaccine if you don’t have it. The risk is very high and would be something to worry about if you punctured your skin with someone that has blood on it, but the mouth, eyes, and nose are low risk .