For a while I've had mysteriously itchy skin which seems triggered by hot showers, temperature changes, and time-of-day. I was told antihistamine tablets (sold over-the-counter for hay-fever) can help, but I have haven't tried it yet.

(Another common cause of itchy skin is being too dry => apply moisturizing lotion twice daily. It doesn't sound like what you have, but I guess you could try).