This is probably a really stupid question .... are you positive that 
all the wet is coming from the eyes?     The reason I ask, when our Toto was that age and her little face became soaked all the way down to her little chest, we were pretty sure she was sick.    After rushing her to the vet, we found out that she was 
teething!     She drooled so badly she needed a bib.     Of course, our vet got a huge laugh because we didn't know!     

      Hope your baby will be OK.