I would not consider a mild rash around the mouth to be an allergic reaction. Babies do a lot of drooling and they tend to get as much food on the outside of their mouth as they do on the inside, so it is probably a reaction to the digestive juices in the saliva. As far as the eczema goes, I used straight flax oil in Allie's bottles. I would probably start with 1/2 Tbsp and see how the baby reacts to it. If it causes diarrhea, then you will need to start slower and allow the body to adjust to the additional oil in the diet.