Yes water can irritate your skin
Some people have more sensitive skin than others and water may irritate one persons skin while it doesn't another persons.
Whenever I take a shower and the water is hard water the skin gets more irritated and sometimes I get a rash on my skin.
From what I've read through research the skin irritation is because of the hard water and also because the skins pores get clogged with the hard water.
If the water is irritating your skin then you may need to use a body wash or facial cleanser that unclogs your skins pores.
Or if you do have hard water then you may need to use a water softener to make the water softer so that it does not irritate your skin.