Most plumbers should be able to handle this, with no problem. Just make sure when you call them that they send someone that has that experience. Well drillers might be busy this time of year, especially if there are draught conditions in your area. Also, I would think that the plumber labor rate would be somewhat less than a drillers. Haven't needed a driller in many, many, years, but they were more expensive then.
A couple of years ago, I woke-up to a winter morning without any water. My deep well pump seized. Plumbers came out and quickly issolated it to the pump, and had all the equipment to raise the pipe and pump. The weight of the water within the pipe can really add up. I think anything over 100' deep requires this tool.
Your problem can range from AC turned off, no-prime, water logged tank, bad or stuck pressure switch, valve shutoff, to motor or pump siezed. Unless something needs replacing, it should be around a 1hr charge. Depends on how they bill travel to a site. They should at least have a very good idea of the problem and the cost to fix, in that time frame.
From your description, it is best to let a pro look at it, plumber or driller, but stay with them and have them explain the major components. Watch and learn, and maybe save from having to call them, down the road.
JohnS