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Most itchy skin spa problems are caused by lack of chlorine allowing bacteria to grow. Bacteria grows much faster in warm spa water than in pools and requires more diligence with maintains FC, including retest after adding to make sure it didn't drop to 0. Also, very high pH and/or TA can be slightly irritating to skin also. TA is best around 50 and pH 7.6 to 7.8.

More here about balancing water in a hot tub, How do I use Chlorine in my Spa (or pool)?

I've used this process for quite a few years now and it works great. I also had some trouble with itchy skin early on. Haven't had any problems in many years and we use it almost daily in fall and winter until the pool opens up.
 
Aha, well that changes things a bit. Those numbers are fine for pH, TA and CH. I would still be inclined to check FC before, during and after when using the spa to see if FC is dropping to 0. Running that temp up to 100 can use up chlorine pretty quickly.
 
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