If i were to push some toilet paper into the toilet to prevent splash then go to blow my nose could i get sick ? i was in a public bathroom, nose was running really bad, so after i did that i blew my nose right after. would i get sick from that?

Did your hands touch the toilet water? If so, there was likely bacteria on your hands. But, if you only blew your nose and didn’t touch any area with broken skin, you are likely not at high risk of infection. If you touched your eyes, there would be a risk of conjunctivitis. Washing your hands before you touch your face is always best. Good luck to you!