说你胖 你还喘上了 来劲儿了 how does this translate in english in this context?
I think it's some sarcastic answer to make him notice how he's full of himself


Yes, that's basically what it means. 

“说你胖 你还喘上了” literally means, "you start (pretending) to breathe heavily soon as you're said to be fat", it is an expression/slang used metaphorically to say someone's pretending to be (more of) something he/she is said to be (usually out of courtesy).

I personally found it as hilarious and offensive at the same time. An example,
A: "You know what, a friend of mine just said you look cute."
B: "Yeah, I actually hear that a lot."
A: "说你胖 你就喘"

Someone "来劲儿了" means someone is pumped. In the given context, I understand it as that B took A's words as an acknowledgement and got pumped.