What the vet will likely do is he will recommend tube feeding which should not be done, everything you need to do can be done by YOU if you are patient and follow instructions to a T (live was one of them)
If you handle, do not offer the proper prey size or type you will get a refusal again, it can take time to adjust and privacy is imperative including during feeding. If you offer too often you will end up with the same result you should only offer once a week.
When you decide to switch to F/T now is not the time you want to thaw at room temp near the enclosure once thawed you want to warm up with a hair dryer grabbing the prey from behind the neck and moving it in the enclosure as if it was alive (I get 100% success rate switching this way).....again now is not the time LIVE should be offered regardless of what YOUR preference is.
A vet will likely take you on a trip from un-needed prescription to tube feeding (which is never needed with BP)
Fixing your husbandry is not something that works overnight especially when a snake has not ate for so long, the less they eat the longer between meals the more emaciated the more they adjust to it and the more it becomes a viscous circle, this is why you should never wait that long for an hatchling to take a meal.
With hatchlings the more you feed them the more they want to eat the less you feed them the less they want to eat.