Your kid should shower after wetting his bed as he will smell of urine if he wet his bed and sheets without a diaper.
If your kid wets the bed they ideally should wear a diaper to contain the pee so it doesn't get all over their clothes, bed and skin.
Pull Ups can also be worn by regular tape on diapers are best.
For kids up to around 8 to 10 years old I would recommend Gentle Steps size 7 diapers which is what my own 7 year old son wears for bed wetting.
We tried pull ups but they leaked on him but the Gentle Steps size 7 diapers are very absorbent and keep him and his bed dry.
Pampers Baby Dry size 7 and pampers swaddlers size 8 diapers are also good for kids that wet the bed.
You should shower after wetting the bed if you soaked the bed and your clothes.
If you've wet the bed and your clothes and sheets then urine will be on your body and you will eventually smell of urine and that would be embarrassing especially if you're around others.
If you or your kid has wet the bed and was not wearing a diaper or pull up then it's always best to shower to get the pee off the body and make you or your kid smell better.
If you wet the bed in a diaper and it didn't leak then you will usually be okay with just cleaning up unless you have to go somewhere such as work or school.
You should shower after wetting your pants.
When you wet your pants you get urine on your body which eventually will smell as it turns to ammonia and it can also cause you skin rashes as well.
If you can shower right after wetting your pants you should do so or at least wash off the urine to prevent skin rashes and you'll also smell.
My 5 year old son wet his pants before and didn't tell me and 3 hours later I smelled urine and he also got a rash.
I made him shower and clean up but didn't punish him for it.
Make sure you change your pants, underwear and shower to get rid of the bad smell of the urine.
As urine does smell eventually.