Uh STD from Urine....?!

Can you get STD from urine if you accidently touched it when your in the toilet? I was using the rest room in an emergency and usually the rest rooms in my school are dirty. I had to go number 2 and i when i was cleaning up i accidently touched someone elses urine on the toilet seat. There was a small cut on my finger too. I don't know if it actually made contact but i am afraid. I immediately got out of the toilet and washed my hands and after that i used hand sanitizer like 5 times in class.
My school is known to be the capital of STD in GA so did i just contracted STD into me?