I had the same exact problem (from the pictures you took, my wrist looked exactly the same) with a medium band. I couldn't wear it more than two days or so without a rash appearing. I didn't believe the issue was related to an allergy since, aside from the fact that I don't have any allergies to my knowledge, the way the rash developed didn't add up.
Initially the rash appeared on the area where the galvanic skin response sensor is (underside of the screen), so I thought the material used for that was producing a reaction. However, the rash then also began to develop on the sides of the wrist, where the plastic/rubbery material is. The rash looked identical, so I figured it couldn't be an allergy to the metal. The other thing that I noticed is that the rash seemed to come on much faster if I wore the band to bed. The rash started to develop after a single night, where if I didn't wear it to bed it took 2-3 days of wearing it before it began to appear.
My thinking was that the rash developed from sweat being unable to dry properly, due to the band being too tight on my wrist. Even on the most open "click" the band was a bit uncomfortable. I've recently replaced it with a Large model (they finally had stock at my local store) and I've been wearing it for 3 days and 2 nights so far with no rash developing whatsoever.
I'll update this if the rash starts again, but I believe my assessment was correct and the issue was due to the band being too tight.