backlash at customer?

i work for a consulting firm and i had this customer ive been supporting and he kept being a pr*ck and kept being obnoxious for the sake of being obnoxious and told me he talked to my coworkers how he was unsatisfied with me, and im the one whos been on his account for awhile and i know for a fact that the coworker he badmouthed me to is also a pr*ck who badmouths me in my back and our manager and everyone in the company and team knows it. anyways it got to a point where he's like: you dont know what you are doing, what is your diploma? then i f*cking lost it told him if he wanted i could leave him all by himself with the other idiot who is actually a cook. yea a fukn cook who works in a consulting firm. dont ask me how he got the job, hes one of those people who fake it til their make it. which is why i dislike him. fake and pretentious. anyways thats what happened and i told my manager and he said it's ok he knows the customer is an ahole. but at the same time im worried now. what should i do?