Is your GP any good? There is one GP at my practice who has a CMPA child himself. I only found this out recently. If I had known I would have asked to see him first as the GP I saw was useless. I have since checked my GP surgery website and the drs actually state any areas (eg dermatology, allergies etc) they have a special interest in.
You clearly could do with some support. It might be worth phoning your doctors and asking if there is a GP or nurse with a special interest in allergies that you can see?
Have you also joined the FB group? They have regional groups so if you also join your regional group they might be able to help you with how to get support locally?
Otherwise if you can't wait till the appointment the only other thing would be to turn up at A&E and literally refuse to leave until they help you. I have heard of people doing that with allergy babies, sometimes it's the only way to get them to listen. There is a risk of your baby getting dehydrated if she won't drink, so if you do turn up at A&E, emphasise how long she hasn't drunk for, how long since the last wet nappy etc. Dehydration can be so dangerous for babies they need to take that seriously and use a drip or tube feed if the baby is dehydrated.
I've also heard of one mum at the end of her tether phoning her HV and saying come with social services and take my baby away I can't cope, it really woke the HV up and eventually the mum got the support she needed. Although perhaps this is an extreme example so i wouldn't necessarily advise this approach.
Has she taken any more milk yet? Fingers crossed for a better night for you tonight.