My daughter is the same way. And I'm sure that it's the milk flow thing. I don't think it's quite as fast as it used to be, and by that I mean a garden hose, so it's probably average but she started to prefer the garden hose!
Anyway. I try to let her just stick her hand on the other side. I push her hand away gently if it starts to bug me (at night, I push her hand away all night). I'm hoping eventually she'll stop on her own. Having something else for her to hold with an interesting texture helps, like we have a stuffed sheep with 100 bumps on it, she touches those instead. She is 16 months.