Glasses are practically a life changer for people who have sight problems. You get older and all of a sudden you can't see up close anymore. Or you're near sighted all your life. Either way, you become attached to your glasses in a way that people who have no vision problems cannot understand. But when the nose piece pinches, it can be a constant nagging pain and you want it fixed ASAP. You do have a few options.
Go to your optometrist and ask them to adjust the nose piece so it's not so tight. If you purchased your glasses there, there should be no charge. Even some optometry shops will do it for free or a nominal charge.
Purchase nosepiece pads from a drugstore or frame store. They are small pieces of adhesive, padded soft fibre paper, much like a heavily padded bandage. But they are exactly the size of the average glasses nose piece. You stick them on your glasses at the nose piece on the side that bothers you -- or both sides, if they both do. They can minimise or stop the pain altogether. And they are inexpensive and come in packages a 10 or so pairs, so you can replace them whenever the padding weakens or they become dirty.
Put some vaseline or other lubricant onto the nose piece for a very temporary fix. This reduces the friction and rubbing, and will gain you time to get to the optometrist or the drugstore.
Don't let the digging go on so long you create an open sore.