Three hours, umm, probably a bit tight. On a fair day you could get from the T7 jetty to LGA airside in 1 hr 30, and if you are a US citizen, green card holder or Global Entry then it's perfectly possible. I guess 3 hours effectively gives you one hour for things to go wrong, which isn't a lot. If this is within AA's Minimum Connection Time then I guess you are protected if there is an irrop, but I'd probably look to do it some other way (e.g. somewehere out of AA's T8 and changing at somewhere nice like DCA, it rarely costs any extra and you just pile up the TPs).

I tend to use the shuttle coach service. You can buy a ticket from the arrivals areas of JFK and LGA (where there are staff running around with handheld ticket machines) after checking what the local traffic situation is like (and taking a taxi if it looks bad).