last july i fell off my bike and hit my elbow on the ground. i waited 5 days to go to a walk-in clinic where they did x-rays and put me in a splint and sling. i had a minor fracture of my radial head and the symptoms you're describing sound exactly like what i had. my boyfriend had to brush my hair for me for weeks.
the first doc sent me to an orthopedist 2 days later who said to take off the splint so it wouldn't atrophy and to only use it as much as i could without being in terrible pain, and to keep the sling on for 6 weeks. it's almost at a hundred percent now, and i only notice an ache when it's really cold or damp out.
i have no insurance so i had to pay out of pocket. the dr.s were very nice to work with me at the lowest cost possible, and the ortho didn't even charge for my visit. i'm mostly bummed that i had to pay over $300 for the splint, just to be told 2 days later to take it off, but i'm really glad i dealt with it because i'm right handed and i could've lost quite a bit of mobility in that elbow.
good luck!