If she's had to be on antibiotics recently, those can kill off a lot of her good gut flora which can definitely cause imbalances in her gut, thus resulting in eczema. Teething can also hamper the immune system (the majority of which is found in the gut) so I would suspect it's all coming into play.
The probiotics she's taking will be crutial in restablishing the good flora. What brand and what dose is she taking? I would consider upping her probiotics a touch for a more therapeutic dose.
Also, have you considered giving her some homemade bone broth to help heal her tummy? We are following a particular dietary plan to help heal the gut lining and the goal is to eventually heal intolerances as well. Here's the basics on meat stock: "Meat and fish stocks provide building blocks for the rapidly growing cells of the gut lining and they have a soothing effect on any areas of inflammation in the gut. That is why they aid digestion and have been known for centuries as healing folk remedies for the digestive tract. Do not use commercially available soup stock granules or bouillon cubes, they are highly processed and are full of detrimental ingredients. Chicken stock is particularly gentle on the stomach and is very good to start from. To make good meat stock you need joints, bones, a piece of meat on the bone, a whole chicken, giblets from chicken, goose or duck, whole pigeons, pheasants or other inexpensive meats. It is essential to use bones and joints, as they provide the healing substances, not so much the muscle meats. Ask the butcher to cut in half the large tubular bones, so you can get the bone marrow out of them after cooking. Put the bones, joints and meats into a large pan and fill it up with water, add natural unprocessed salt to your taste at the beginning of cooking and about a teaspoon of black peppercorns, roughly crushed. Bring to boil, cover and simmer on a low heat for 2,5 - 3 hours."
Remove the bones, leave in all of the fat that accumulates in the broth. The fat is a very important healing property. You can give it to baby in a cup or bottle, even mix it with BM/FF. My little guy likes it best if I give it to him with a medicine syringe. LOL! It really is a healing food though!
For the external itch of eczema, you could try putting some pure, organic coconut oil on it. Coconut oil is very high in lauric acid (the same healing compound found in breast milk) I put Coconut Oil on DS2's rashes and it seems to really help.
Besides that, epsom salt baths can help the external component of eczema as well. Be sure to use at least 1-2 cups in a full warm bath. Let soak for approx 20 minutes if possible. No soap. Epsom salts help to restore the natural PH of the skin so it can heal.
((hugs)) hope it gets better soon.
