Go to the nearest Interstellar factor, who you will find at a station in any low security system. You can pay it off there rather than go all the way back to the system where you got it.
Fines don't count for anything, so you can leave them as long as you like and pay them off when convenient. You're bound to go to a low security system sooner or later, so sort it out when the time comes rather than wasting time now.
When it says you can't get some services, that's only at the station where you got the fine. If you need anything from that station, you can still go there and pay the fine on arrival to restore all services.