Yes the "mouth guard" is a splint. I prefer the ones that go on the lower teeth, as I have trouble breathing at night with the upper splints. You can go to a sports store and get one like the football players use, heat it up and mold it to your teeth... and wear it at night. If nothing else it will protect your teeth from the grinding...but it might also help with the muscles giving them room to relax... it won't be as good, but for the expensive one, make sure they make good measurements to put your joints exactly where they need to be for relief.
I don't know about insurance companies covering or not, as my TMD was caused by the accident and therefore all of it is covered...including my veneers I had to get less than 2 years ago....because of the bruxism over the years wore my teeth away.
IDK about the ENT..you can ask them on the phone if they can help with TMD.
Good wishes.