This will sound strange, but eat salmon. I used to suffer from this and over time noticed it had gone. I happened to read somewhere about the benefits of eating salmon and this was one. I had recently changed my diet and started to eat salmon a few times most weeks. This is from the diet doctors website.

One in three people have a condition called keratosis pilaris, which is rough skin on the back of the arms that feels like goosebumps. It's caused by extra keratin accumulating in the hair follicles. Sometimes it can affect the back and chest and, in less common forms, the face and eyebrows too. In extreme cases it's sore and itchy.
But good news is you can get rid of it through a change in diet. It's a fatty acid deficiency so you need to eat more oily fish. Vegetarians should eat a handful of linseed every day or use linseed oil in dressings. To supplement your diet further, take multivitamins and omega-3 and -6. You will probably see the change within the first two weeks!

Try dry skin brushing before showering and then follow with Soap & Glory's excellent Firminator cream - great fro thighs too!

I used a salt rub and a brush every day for 10 days. It took time to do every morning but it really smoothed out all those bumps under the skin at the tops of the arms - and I was glowing for my hols.