I'm pretty sure that is very normal. Babies have major growth spurts at 3wks, 6wks, 3mo, and 6mo. Sounds like your baby is around the 3mo growth spurt. When they are in a growth spurt that have a couple days of major sleeping and also a couple days of major eating. As long as your baby seems normal besides the sleeping I wouldn't be concerned. Always check with your ped though if you are really concerned.
As for the tear duct, my daughter had the same thing... with both of hers but it was cleared up within a couple months. I rubbed them any chance I remembered to, so it was at least a couple times a day (of course definitely make sure hands are clean!).