When the weather isn't too cold and might change during day I wear a jumper/sweater on a T-shirt, my arms get really irritated. I heard this is what happens coz wool in the sweater irritate the skin. Is there any way to protect arms from being itchy and red while wearing a sweater on a T-shirt?
I have this problem too.
My only answer is to wear a long-sleeved cotton shirt under my woolly pullies. You can try a long-sleeved T-shirt or a dress-shirt with collar.
If it's a proper shirt with a collar it stops chafing around the neck too.
Turn the jumper inside out, line the sleeves with material that doesn't irritate you (like whatever your tshirt is made of), sew it in, turn it the right way back, and wear
be mindful of what a jumper is made if and how it is knitted/woven when you buy it. Some materials and knits/weaves irritate more than others. Identify the problem and avoid those types of jumpers when purchasing. Replace the jumper with a less irritating one, perhaps give the irritating one away (to someone you don't like? :) )
Years ago, people used to use Goose Grease for this purpose
It forms an insulating and protective layer
For various reasons this has fallen out of favour, except in Switzerland where the use is still prevalent