Also forgot to mention - I have a little pain-uncomfortable feeling on my penis today...
This is extraordinarily low risk for any disease from the splash on your penis. Zero risk for anything like an STD, and a very minor concern of a common bacterial infection, if you had any open cuts or sores on your penis. If you do not see redness and swelling anywhere on your penis in the next few days, forget about it and move on.
Biting your nails has nothing to do with anything, but if you didn't wash your hands after being in the toilet, you could transfer bacteria to your mouth and become ill.