Sure sounds like hard water. This is what you want OP. It's an inline shower filter. Affordable unit, economic filters and works a charm. I recommend it based on personal experience. I don't know if my link is the best price and you may be able to find a better version if you do some searching. Heres to happier hair!
I had a similar issue. My skin was very bumpy with uneven texture, some breakouts and just dull. It always seemed that after my shower it would be red, splotchy and worse. I used tons of products and got a routine down but I was just minimizing the worse and my skin always looked bad. I've been to the dermatologist and am on tretinoin, but still my skin was bumpy, broken out, and awful.
A few weeks ago, my aunt bought me a shower filter I've had on my amazon wish list for about 3 years or so. I would never believe this myself, but after my first shower, my bumps were gone. It doesn't even make sense to me. Seriously, 90% of my skin problems instantly cleared up. The other 10% is slowly clearing up and for the first time in 9 years, my skin has a bit of a glow, it's smooth and soft, and the grainy unevenness is gone. I have not changed one thing in my routine and it was an immediate difference after showering the first time.
I wish I had realized that my skin got so bad after I moved to this apartment 9 years ago but I never saw the connection. We have well water here and the pH was fine with a fish tank test. I guess there's something else in our water that is breaking me out and having the filter remove it is some sort of miracle for my skin. I have this model and the filters are less than $15 about every 6 months to a year depending on your usage. I highly recommend trying it--I wish I would have bought one years ago.
I had a similar experience and found this shower head filter helpful. still not as great as before I moved, but better and my hair is getting used to it now.
Buy one of these for your shower, it might help. Tucson has really hard water.
Culligan ISH-100 Level 2 Inline Shower Filter https://www.amazon.com/dp/B000MVYRWE/ref=cm_sw_r_awd_bBGjvb0VT7600 https://www.amazon.com/dp/B000MVYRWE/ref=cm_sw_r_awd_bBGjvb0VT7600