Is the Electrician trying to scam me?
Quote: "The bedroom outlets that I tested were pulling 36-49 amps."

Sounds fishy. Outlets do not pull any amps by themselves. Did this electrician plug in to the outlet with some kind of test load to draw this power? If not, the electrician is probably not honest or does not know their job. I was an electrician for about 10 years, granted that was 30 years ago but I have never heard of testing the "amps pulled by an outlet" since outlets do not "pull power" at all, only the load (your lamp, tv, or whatever) plugged into the outlet "pulls power."

Finding the breaker at the panel is easy: 

This paragraph assumes you have only one breaker panel and is a good place to start if you don't happen to know.
Plug a radio into one of the outlets in question and turn the volume up so you can hear it from the breaker panel. A lamp works also but you have to run back and forth to check if the lamp is on.
Turn off all 15 and 20 amp breakers one at a time. You should hear the radio go silent when the proper breaker is turned off. If there is still power to the outlet(s) in question after all 15 and 20 amp breakers are off, then it would be logical that they are not wired properly and may well be wired to a higher amp breaker. Skip the next paragraph in that case.

If you found the breaker that controls the outlet(s) in question you can replace the breaker if you want to be sure there is no problem with the breaker.

If the outlets are not powered off after all the 15 and 20 amp breakers are off, then try the higher amp breakers one at a time until you find the guilty breaker. THEN, be sure you do not have a sub panel somewhere that is fed by that high amp breaker. If you do, then you need to start over with that breaker panel.

BTW, even if there is no "amps problem" you may still want to open all the outlets and check them if one had melted insulation. That is almost always caused by a poor connection or nicked wire. The outlet was likely not installed properly to start with. 

Another reason the outlet may have failed, since the electrician claimed that it melted from the inside, is that a heater or other high draw appliance was plugged in loosely. That would cause the same problem as a bad connection to the outlet. In fact it would be a bad connection, just that it happens to be the plug, not in the wall wiring. If your outlets are worn out, that is, you feel little or no resistance when you plug something in, they are a fire waiting to happen when someone plugs a space heater in.