If you suspect a problem with the oatmeal, immediately remove it but don't change anything else about his diet. If the problem goes away, and it occurs at the same time as the disappearance of the illness your daughter has, it could be either. After a good week or two, re-introduce the cereal. If it happens again, discontinue for at least 3 months until his system matures a little.
Anytime you make a dietary change, go slowly. I wouldn't jump in right away and call it a true "allergy" but it's wise to be gradual if you suspect a problem.
There's also a fantastic children's supplement (no warning labels, no drugs) that will probably eliminate any dietary issues or allergies in a gentle way, and also provide optimal nutrition. It's great to not have all those colds, flus and virus stomach-bug things anymore! Let me know if you want more info on that!
On breast feeding - as long as he's enjoying it, keep doing it. It's important nutritionally, and also emotionally for both of you. It's such a special time as long as both mom and baby are feeling positive. It's not so much about the quantity especially because you are mixing breast milk with cereal. Sounds like you are doing great! Once they eat solid foods, they can go longer without eating/nursing, and they just take in more at each feeding. That's good - also helps them sleep thru the night! I don't think you can overfeed - at this age, they stop when they are full.
Good luck!