Both my girls had it. Neither had any side effects. It doesn't sound like a side effect of the vaccine to me. Most of the time the side effects clear with in a few days to a few weeks after the vaccine is given.
As babies grow and change, so their schedules. Of course his BM is watery, he doesn't eat any solid foods yet. My oldest was exculsively breastfed and she only pooped once a week. When she did, she pooped ALL day long! My youngest was exclusively breastfed and she pooped every day.
The symptoms you are talking about sound a lot more like gas than rotovirus. You can try a few simple things. Bring his knees up into his chest about 10 times when you notice hims squirming, it helps release gas. Try baby massage. Mylicon drops works wonders on a gassy baby too.
Make sure he's not gulping too much air when he's nursing too. Sometimes as babies get older, their latch changes, especially if he's getting more curious as he nurses. My girls were both easily distracted at about that age.
If you're really concerned, call the pediatrician. That's what they're there for!