My limited experience with pet skinks (EWS and BTS) indicates they can go downhill VERY RAPIDLY if you don't get on top of this kind of illness IMMEDIATELY with proper medications and they can be dead within 24 hours of first showing symptoms. If this alarms you, good, it'll get you to take action ASAP or sooner.
I didn't know it the time , most good herp vets will see urgent cases outside usual surgery hours and have an afterhours contact number for just such emergencies.