Touched a cup that wasnt mines by the lid the cup was very wet i have a cut under my nail bed will i get some kind of finger infection (scared to use the bathroom because i dont want to touch my genitals to wipe?

What you describes does not put you at risk for any infection. Go to the bathroom, as you need. Have a healthy diet, exercise 30 minutes/day, drink plenty of water daily so your urine is mostly colorless, have safe sex, no tobacco alcohol weed or street drugs. For nutrition: http://www.choosemyplate.gov/. Get HPV and Covid vaccines. Wish you good health!