Have pain tapping top of tooth, told dark area under root, infection absess.2nd dr says no b/c vital nerve and +cold test means no infection. Is fact?

Painful tooth. Need more information: does the tooth have a large filling, does the tooth have decay, how long has the tooth been painful, when does the tooth hurt (chewing, not chewing, hot and/or cold), what is showing on the x-ray? At this point, you should get an opinion from an endodontist (root canal specialist).
Tooth. From what you have described it sounds like you may have a small abcess on the tooth which at this time may not be causing any problems. You need to see your dental provider and ask about evaluation for a possible root canal. The tooth may still be vital, but in need for a root canal which would explain why the tooth is not cold sensitive. Either way you need evaluation by your primay dentist.