I just looked at the picture of the recessed light and read all the comments. Well, I need to replace the socket but I do not know what the name is and where to find this porcelain socket...Help please
Lamp components are fairly standardized. You should be able to go into a quality hardware store and get any common part. If the parts are not common, it may be possible to rearrange it with common parts.
One common problem is people overlamping fixtures; that is, putting too-high-wattage bulbs in fixtures that can't take the heat. This is a great time to alter the fixture to make that impossible, by changing to a socket type for which high-wattage incandescents are not made. A good choice for this is a candelabra base, as LED screw-in "bulbs" are widely available at sane price, including some quite high-brightness ones.