It's hard to say about the sides...today, he was biting equally on both sides. In the past, I think he may have bitten more on the right (which tends to be the breast with a larger supply, stronger letdown). But, I think it has been pretty equal between sides.
Over the past 6 months, the biting has been sporadic. It's been pretty consistently because he is playing (why he thinks this is a game, I don't know--I've never encouraged it or responded in any way other than saying no, or yelping in pain--I've never given a joke-y response, not once) or because he is done (or, I think he is done). He hadn't been biting for most of the cold and actually now seems to really be over the congestion. But, now he is biting a LOT. Every nursing session, both sides, at the start of the session, in the middle, all the time. Sometimes it's a nip on the tip of the nipple (this kind of biting has, historically, been "play;" sometimes, it's a full on bite on the whole thing. He's doing even in when he is nursing to sleep, which he has NEVER done before. He also seems to be scraping his teeth when he is latching on, which is also new (but, this doesn't hurt).
I will try to give him something cool before nursing to see if that helps. And, yes, he does let me hold his hand, sometimes. I can do that for some feeds but not for the ones where I am walking him to sleep. Maybe I'll give a lovey a try again--in the past that's kind of wound him up (he doesn't calm down enough to go to sleep), but actually, I think I'd rather get the nursing in bite/twiddle-free and then walk him to sleep sans nursing than nurse him straight to sleep with bites and twiddles. I've been reluctant to do this because he and I really struggle with getting him to sleep without nursing (he can get to sleep fine with my husband without milk but not me). I think he is so used to nursing to sleep with me that he just has a serious association that is hard to circumvent but we can work on that too.