Indeed, why walk in public, you must at least retire.
But seriously, you can't even imagine how many people experience similar problems! I didn’t go into the details of the reasons, but I think they are all different: someone has shame, someone needs comfort, someone has a ritualistic action and cannot happen anywhere.
At one time I solved the problem like this (the reason was shame and embarrassment). I ran into a public toilet when there was no one there and tried to do everything as quickly as possible, without witnesses. Anything is better than enduring and suffering. Over time, the psychological barrier went away, when it came to the understanding that there is nothing terrible in all of this.
And you don't have to walk around in public - they won't understand and condemn. Although this is natural, in modern society it is customary to hide the departure of natural needs. So your discomfort is understandable and explainable and you are doing everything right.