Hello!
My little boy, Mateo, is also 4 months old, used to do this sometimes too.
He arched his back started to cry after what only seems like seconds... The lactation cosultant and I figured out that it was because he was impatient and couldn't wait for the letdown, and the reason why he would latch on to the other breast and suckle so quickly is because the letdown was faster!
The way it was explained to me is that once he stimulated the first breast, even if it's less than a minute, then the other breast is pretty much ready to go, which is why once I switched sides, he would suckle and just like that the let-down would happen.
How did we fix this problem? First I began to take "fenugreek" and to pump after each feed to increast milk flow, plus I wouldn't wait until he was starving to feed him. He started to eat every 3 hours on the dot, and we worked on extending the feeds past the 5 minute mark since he would think he was full and stop nursing. (a snacking issue!)
We've moved past this point now, since he nurses for about 7-10 minutes on each side now and is on the 4-hr EASY routine. He eventually learned to be a better eater rather than a snacker.
I hope this gives you some help.
Oh Mateo is now starting to put his fingers in his mouth while nursing too, although he doesn't cry when I move them away, this, I was told, is a teething issue.
Take Care
Nayade