I have posted on here before. My son is nearly 5mo, exclusivley bf, and is sick periodically throughout the day. This has been going on since he was born, and dosen't seem to be getting any better. It dosen't bother him and he is putting on weight, I am just concerned when it will stop, and plus what it is going to be like when I wean him.
I think some babies are just sicky babies tbh! My ds (also bf) has been the same as yours, and he is 6.5 months. I have a friend whose baby is 10mo and been on solids since he was 19 weeks & ff from birth who is also quite sicky! If he seems happy and content, not in distress, gaining weight fine then I don't think there is any need to do anything but to have lots of bibs and muslins at hand. Have you spoken to your HV about it?