Hi Delia, it is not that uncommon for male dogs to have part of their penis protruding from the sheath on the odd occasion but it is more of a worry if it is unable to go back without assistance. Did the vet offer any advice when you took your boy in to the surgery about this?
There is a link here which gives some information you may find helpful:
https://www.petmd.com/blogs/thedailyvet ... ment-30463
I can also tell you about our experience with one of our male dogs and a similar issue although in his case this did become very serious but may well not be the same situation as with your boy. Our dog has been neutered for over 4 years so neutering is very unlikely to be of any help at all and would not be a solution to the issue. Apologies for the lengthy tale but it does highlight potential issues for any male dog that does have difficulty retracting his penis and it can be more than just an embarrassment.
With our boy, from adolescence onward he frequently had the end of his penis protruding when he was resting and awake and, as I was worried about potential infection etc. we took him to the vet. We were advised at that time not to worry about it as it was just "one of those things". Then, a year or so back, I thought he was not right in himself and, as he had been constantly licking at his private parts, I thought he might have a urinary infection. Watching him when he pee'd I saw blood dripping from the end of his penis - too much blood for this to be just an infection. He was taken to the emergency vet (weekend) who thought he may have scratched his penis and this was causing the bleeding. A return visit to the vet when the surgery re-opened and an examination under sedation revealed that hair had been drawn down inside the sheath and wrapped round his penis and was cutting into it like cheese wire. I cannot imagine how much pain he must have been suffering. The vet removed the hair and all was well for a while until, earlier this year, I was sure the situation had recurred although there was no bleeding to see. A further examination confirmed that hair was again wrapped around and cutting into his penis. It seemed that the end of the sheath in his case was inverted and hair was growing on the inside which meant it was not accessible to us for trimming - he would need to be sedated to cut it. Although the vet was happy to deal with the issue, we were reluctant to just leave it at that, given it may keep recurring and we made the decision to allow the vet to cut open the sheath and remove part of it to allow us to monitor and deal easily ourselves with any hair that might get caught, although the surgery was intended to help prevent this. So far all is well thank goodness!
I do know from the vet that this is a pretty rare event so I don't want to alarm you that anything quite so serious might happen with your boy. If the vet has not given you any advice, I would just monitor your little one to make sure if there is a problem you can get him to the vet quickly. If it is just a case of you helping to retract the penis and you can do this, it may just be a bit embarrassing but may eventually resolve itself.
I would add though that if your boy has had an "erection" in that his penis is fully out and swollen in size, this is something that can take quite a while before it will retract anyway and is quite normal. It happens most frequently with entire adolescent dogs although usually when they scent or are in the vicinity of a female dog in heat. You would just need to give him time to calm down and it will resolve without any need for help.
As regards neutering, it may depend on the individual dog as to how long it would take to reduce the sexual urges which can contribute to incidents of humping / getting an erection but it will not have any effect on how easily (or not) a dog can retract his penis as this is a physical issue rather than a hormonal one so neutering would not help in this situation.