Getting a second opinion is always an option though you may have to pay for the appointment yourself. The management of elbow injuries can be complicated. Your symptoms suggest at least one of the nerves may have been compressed. Weakness and numbness are symptoms of nerve involvement.
A wait-and-see approach is often best with mild nerve injuries. Testing nerve function too soon doesn't always give all the needed information. It takes time for the degree of nerve injury to show up.
Most mild nerve injuries heal by themselves in one to three weeks. A more moderate injury may take up to six or eight weeks. If the nerve is damaged beyond repair then surgery may be needed. Most patients have excellent results if the repair is done within 12 months of the injury.
If you know there are no fractures then you are probably safe waiting to see if the nerve will heal on its own. Full recovery takes about 18 months when the nerve has been cut through. It doesn't sound like you had this type of serious damage so a little wait-and-see time is appropriate.