Square, ours is excema on the face too. It started after I gave her some ratatouille and she spread the vegatables over her face - within half an hour she had a red rash on her hands and face. I think this was caused by the acidity of the tomatoes and is apparently quite common. However, within a couple of days she developed excema where the rash had been. I don't know if that is just a consequence of the tomatoes or if it relates to a delayed reaction from eating all the other foods I'd been giving her before including dairy, egg, wheat etc. I've been advised to take her off all common allergens and once the excema has cleared, to start reintroducing one group very very slowly. In the meantime we've been referred for tests to see if she is allergic to anything.
Before this happened, DD wasn't eating lots but was getting a good mix of foods. Now she seems much more enthusiastic about food, really ready to tackle it, and I feel hampered by the limited diet she is on!
All that aside though, the fact she is now so enthusiastic about eating is very reassuring. She's just turned 8 months and until a few weeks ago, wasn't that interested, which made me really doubt whether BLW was right for us. Now I'm pretty sure it is so that's one aspect that seems to be going right!
Sorry, that wasn't meant to be so long and waffly....
Glad your dd is getting on well and hope her excema starts to improve soon. My GP and HV seem very taken with the idea that dd's excema is food related, and as her skin was fine before weaning, I'm inclined to agree. But saying that, I think excema can be caused by other things too so your doctor could be right.