That's a good one, and I used to experience it too. Sorry folks, to get graphic for the following -- how do you talk about something without just going ahead and talking about it?
I didn't pee in the water in earlier days because I just didn't want to mess up my suit. Fact is, when you have to go, you have to go. I used to have an agony holding it, then on shore rip my suit off, and desparately get to the head, beach, hedge, or whatever. Damn near killed myself if the suit hung up on my feet and/or I did get that suit off without someone tugging me around like a guy behind a horse in an old western until the feet came free... But I'm older now, and have found an exquisite suit shampoo...
Seriously, first time I gave up the fight and let it go in the water I was ab diving, probably 100yards from shore, nice calm sea, with my buddy Tom. Enough was enough. There was no going back. I started to pee, and I swear, I suddenly felt, full body, as if I was SERIOUSLY going to be punished. What a wierd reality. Suddenly, I was like two people. One was the guy, with a sudden relief and VERY warm suit. The other was about to really get it. I remember saying to Tom out loud, "you won't believe what a bizarre thing I'm going through in my brain right now, and I was busting out in laughter even though feeling doomed. Like, I was saying, yeah, my mom is going to run out and yell at me right now or something. So perhaps it was a flash on early bathroom conditioning. Hell with it, I learned, this urge and pressure happens out here and just has to be expected to happen. But it took about six dives before I finally acclimated. So heck, if it's about your suit, get a great shampoo at the dive store, and to to Target or somewhere and get a big 100 quart storage bin with lid (can keep extra gear in it when not diving too). Turn your suit inside out, get it in the bin and poke it under the suds to agitate with the blunt end of a broom stick. When done, use a good blasting nozzle and hose your suit over a patio chair to hold it open well to seriously blast rinse, and you are in business. There are enzyme solutions they sell also at dive shops and also pet stores to really get into the pores of the suit liner, but I haven't ever found that necessary.
If it is an 'inner' thing, and your suit isn't the issue, but simply relaxing is, then no kidding, get a little distance from your buddy, and out loud (quietly, you don't want anyone to think you are nuts) have a little conversation with yourself. Even call yourself by name a few times, and say it's ok. Just literally reassure yourself with some repetition. Ever help out a pet, or a little person when they needed help? So if it is psychological, there's little more effective than simple, direct sincere communication. Just 'get your arm around your shoulder', and talk to yourself...talk yourself through it. If you want to do tough love, discuss how it will look if you hold it beyond capacity... and hear the popping sound and see the chunks of meat and flying bones when you finally explode...