Mother has a lip cold sore, but takes medication for it. after she touched it, she gave me a cup. i washed my hands after touching it once but continued to use it. i went to the restroom and accidentally touched myself when wiping. will i get herpes?

No doubt Herpes is contagious but the way you are describing , most likely you should not get the infection so quickly. If symptoms start ,you must see your Physician.

Low risk from any one episode but certainly possible. More episodes = higher risk. Prevalence world wide = 60-90%, higher in low income countries, progressively lower in higher income countries. “Usual” mode of spread is direct contact - lip to lip or via saliva. But certainly can be spread by touching or on glasses, cups, etc