Will I have enough time to catch this flight at LGA from the Upper East Side?

You'll likely be fine, but I'd feel better if you left at 4:30 pm. This would give you a bit more of a buffer in case of unexpected delays.

It's possible but tight. Google Maps is estimating that leaving from there today at 5 pm could take anywhere from 28 to 60 minutes, which would mean you'd arrive at 6 pm. If you have priority access to get through security, 90 minutes from curb to gate might be enough. However, it's tighter than I'd prefer, and I'd only do it if I had no other choice. You might consider taking the R train to the Q70 bus. Whether subway delays or traffic jams get the better of you is anyone's guess.