The skin swells and gets puffy but the pad doesn't seem too tight? It may just be too large in terms of area. The ulnar nerve doesn't have a real big area where it's exposed.
I've never pinched mine but I hit it very hard once in an accident. My arm from the elbow to the hand felt like it had been shocked and burned. It took a few weeks to get back to normal.
Did you try some different types? I think the neoprene type is pretty uncomfortable. The old fashioned pads with adjustable straps are pretty comfy and you could cut it down to a more comfortable size.
http://www.healthykin.com/showproduc...FVBgMgodLHkAog