Warmog is fine on Braum, but Sunfire is probably a better option here. He has literally no armor. Whether this was a situational decision we don't know but the bottom line is that there's going to be at least one AD character and they will be laning against you. If you really really want health then Randuin's is fine too.
After getting rid of Warmog, you have to rethink Spirit Visage too. Banshee's is good, but so is Locket, and Locket is more fitting to being a support.
But really if anyone on their team had a blade of the ruined king you'd be in some trouble.
And you should really be buying at least one item with a shield attached to it.