My mouthwash bottle came sealed with a plastic around its cover. Assuming I do not rip the letters, am I permitted to rip the plastic off to open the bottle, just like it is permitted to open up a bag of potato chips on Shabbos.

ב"ה Shalom, You may remove the plastic not along the perforation in a way in which the seal is ruined. In regarding to the tearing of the letters, there are opinions which hold, that tearing letters is not the same as actually erasing them and therefore when in great need, one may tear the wrapping even if letters get torn since that is not the person's intention. However, it is preferable to be stringent. שמירת שבת כהלכתה (א), פרק ט, הערה נא, פסקי תשובות אורח חיים סימן שמ אות י, All the Best. Chag Same'ach.