This is called Urticaria. I'm living overseas now. My daughter also got this problem when she was 4 months old, & it last till she was 7 months old. When she got it in the first place, we were in HK. The rashes appeared in the morning, then gone away at the evening. But, she was quite serious, as the rashes kept coming & going away very frequent. At that time, I brought her to see many doctors, even a professor. I spent a lot of money on this. They also said that it's caused by the milk formula, & allergy to some foreign material, this & that. I was suggested to feed my daughter soy formula. But, she still got the rashes. Then, I thought she might allergy to the other things. I was so worried as I don't know what was she allergied to. I threw away many baby clothes that I suspect it caused her skin problem.
Until she was 6 months, we flied back to overseas and I brought my daughter to see the paediatrician. The doctor said it's urticaria. Some babies will have this. It's not caused by any food or things. It's incurred from the body system. It will go away later when they grow a bit elder, but no one knows WHEN. The doctor said it may or may not itchy. If it does bother my daughter, I can feed her Zyrtec. But, it only helps temporarily. Since I couldn't see my daughter have any uncomfortableness, I didn't feed her Zyrtec. I haven't seen any urticaria on my daughter since she was about 7 months. I hope it's gone forever.