How long will it take for an inflamed large pimple without a whitehead to go away? is it a papula?

Usually a few days: Large pimples that do not have an outlet like a whitehead, may represent significant inflammation under the skin, and sometimes the presence of pus underneath. Some pimples may actually be a cyst related to certain sweat glands. A papule is a swelling of the skin of a certain size that may or may not be a pimple. Try not to pick or pop it as that may make it worse. If it gets bigger see doc.

See below: Agree with Dr.B. In addition to his advice, you may try warm fomentation to facilitate maturation of the pimple, if it is a pimple.