I've been having numbness in my left ring an pinky finger the past 3 days. The week prior I had severe pain in the area behind my elbow. This tells me it's a pinched nerve. Is there anything I can do without going to a doctor?

You might try .. .... an over-the-counter wrist splint. I concur with your diagnosis that some nerve compression is going on, and it may be at the elbow, but even stabilizing the ulnar nerve (suppliers of the 4th and 5th digits) at the wrist could help. Anti-inflammatories such as ibuprofen/naproxen could reduce swelling if this is part of the problem. If it goes on a week or more, you should contact your doctor.