I am not entirely sure what this is, as most reactions to showering tend to be more diffuse and not just limited to 1 or 2 spots. Luckily, if the symptoms are not persistent and are not occurring except with showering then they are unlikely to be a serious problem.
I think the most likely thing is that that you are having a minimal contact reaction to something you use while showering, such as a brand of soap or shampoo. You could experiment with changing brands to see if this resolves the issue.
Another possibility would be that these are hives
. Hives, or urticaria, can occur in some people related to certain physical stimuli, such as scrubbing or hot water. As long as these do not generalize it is not a problem. A few hives could be treated with an antihistamine like diphenhydramine, which is available over the counter. You could also try limiting scrubbing and using less hot water.
Regardless of what is going on, I do not think this is serious. If the symptoms worsen are become more persistent, you should talk to your primary care doctor
to determine if you need a better treatment or workup for an underlying condition.