Errin,
Unfortunately, a toddler cannot tell you what has happened. He could have injured the hand, this would give you the swelling, but not the fever. He could have been bitten by something, which could cause both symptoms. This is not the typical presentation for an inflammatory arthropathy, but that could also cause both symptoms. A local abscess could cause both the fever and swelling. A rare cause could also be a thrombosis in one of the major blood vessels. As you can see, it is very difficult to determine what it is, especially when the patient cannot tell you exactly what's going on. Pediatrics is truly close to veterinary medicine sometimes.
However, the problem is, that if the pressure in the hand gets high enough, it can cause the muscles to die. This is called a compartment syndrome. If the muscles die, then the hand would be useless.
Unfortunately, there is not a lot of time to waste in a compartment syndrome. As even a delay of a few hours can cause irreversible damage.
So, even though a firm diagnosis of what is causing the swelling, the symptom of the pressure has to be addressed quickly. After the pressure is released, then the original cause can be sought.
Wishing you and the little one the best. Good luck