No. If you're concerned, take a test and see for yourself.
Well this is the situation. The other fighter was on top of me and he elbowed me right above the eye causing me to instantly open up (the cut was somewhat deep and i needed stitches) anyways while he was on top punching me i managed to punch him where he had the headbutt cut and then he put his head down and his blood litterly dripped to my cut. Is there still no risk there?
No risk, you're fine. No worries.