the cause of lacrimation can be checked by making a tubular (lacrimal-nasal) test - when a special dye (fluoresicin or collargol) is instilled into the eye and see if there is an outflow into the nose. If the dye appears in the nose, then the "nose is not clogged", if not, then there are problems with the patency of the lacrimal passages and it needs to be restored.
Regarding the clogged nose, it seems already answered. And according to the turned eyes I will say this - it depends on where they are turned. If on a clogged nose, it is bad, but if in the opposite direction, then the pupils will strengthen even more.