@Wizzy unfortunately when you're a minor you parents have final say when it comes to pets, it was the same with me so I understand your difficult situation.
As you're noticing problems, bringing her inside and wanting to do something about it then that shows you're not a bad pet owner. You care about her.
Making sure they have hay and water is the most important thing.
Chewing bars can be a sign of boredom. Could you possibly get her out more often and let her wander around your room supervised? How about making her a toy? I give my boys the cardboard inside of a toilet roll filled with hay, or a paper bag or cardboard box.
In regards to her snuffly nose, it could be an upper respiratory infection, which needs antibiotics. But I understand that your mum won't take her. All you can do is monitor her closely and tell your mum if/when she gets worse. Offer to pay for a vet visit yourself with pocket money, or offer to do chores around the house to cover the cost.
If you can, weigh her every few days, at the same time. That's a good way to detect if pigs are ill.
