Child Has Protrusions On Skin, No Redness Or Itching. Which Test To Do To Identify Problem?

Thanks.
My son is 17 years old and when he was around 9 or 10 years he started showing some small protrusions in the skin like a common allergy. It all started in his hand, then slowly started spreading to face , to other parts of the body. It will suddenly vanish from one place just to be found at another place. there was no redness or itching ; it simply made the skin look rough. We got him treated from homoeopathic medicine which he took for nearly 5 years. As long as he took the medicines, the allergy would subside and once stopped the medicine, it will increase. Finally we were fed up and left it as it is. Now his front (chest and abdomen) is fully covered with those allergic protrusions. What kind of test canbe done to identify the problem?