You should relax. Nothing is gonna happen. IP address is NOT enough to link you to your real account, because one IP can be used by thousands of people.
Trust me on this one, relax and next time use some anonimity measures.
According to the law PayPal can not link or associate paypal accounts just because of the same IP. They would need to conduct a proper investigation, but they ain't gonna do it because it would cost many many times more then the -125 dollars that you owe them. Just forget that account and never log into it again. Also clean your browser history, cookies and delete the router logs if you have them enabled.
If this was a much larger amount or you would have done something more serious and they did conduct an investigation, your computer and networking hardware would be checked so it doesn't hurt to get rid of all traces. So even though they would know that same external IP was used, they would have no proof that it was you who both accounts belong to. After all, you could say maybe some random guy cracked your wifi router password and used your connection to do that stuff.
But in this specific case I doubt they would bother to do anything. 125 dollars is absolutely nothing for paypal.