@ehdog

Showers can easily raise your heart rate for a lot of people. As long as it wasn’t random and it settled back down after, then yeah, that’s normal.

@ehdog There is such a thing as POTS, or postural orthostatic tachycardia syndrome. It's well known, and some of that may be at play for you. But as Wala says, everyone's skin is connected to the parasympathetic nervous system and getting into a hot tub/bath or into a hot shower will almost certainly cause a rise in HR. However, it 'should' normally begin to subside as your mind and skin get used to the unusual sensations of both temps and beating waterdrops. So, if your rate is still elevated by the time you're stepping out of the shower, I would want to get that looked at. If it subsides within a few minutes back to normal after you've toweled off (which is often a rather vigorous activity for most of us, especially north of 65) then I would say it's 'normal' for you. What you should be concerned with is a sustained high tachycardia for no apparent value (keeping you moving quickly or lifting/moving things that need both hands, etc).
I'm no medical expert, but I thought I would mention POTS, as unlikely as it would be for you just in showers....but we never know. The body knows.