I have dry skin nummular eczema, so I know a bit about treating dry skin. ;-)
I wouldn’t use the hydrocortison cream if you don’t have eczema, but if you do have something that resembles a rash/eczema, it could help to use it next to a base cream like cetomacrogol cream (I think it’s called the same in English as in Dutch, but if you can’t find it, let me know and I’ll have a look).
I mainly use the cetomacrogol cream a few times a day on my eczema patches and another cream for dry skin on the rest of my body, because the other cream will absorb better (this is very individual). Hydrocortison is a class 1 corticosteroid, which is the weakest. The rest is prescription only, as it can cause your skin to thin if overused. I am currently using a class 2 corticosteroid on my eczema (I had a flare up from the diuretic effect of drospirenone, so hrt related), but my eczema is not clearing up completely, so might need a stronger one this time.
With a good moisturizing regimen, I had been eczema free for about 20 years, but I’ve had some reoccurrence since in perimenopause (treatable with the base creams up until this flare up), so low estrogen is a big factor for me too.