I have the same issue, From what I understand it's quite common with male Boob growth and some females.
The only answer I found (not a complete answer, but it helps) is to wear a bra with side support, they're hard to find (especially in "male" sizes), or failing that very careful use of body tape (ouch!).

I was thinking of trying a strapless (adhesive) "cleavage" bra; easier to get, just not sure how long they'd stay attached.