@Mummybuttons23 my thoughts are with you because we've had a similar battle. Maybe not as much with the eczema (she had eczema when she was on 'normal formula' but it cleared up when put on Aptamil Pepti 1. But that's the only symptom that has improved with the Pepti 1. Apart from that she is constantly in pain, refuses feeds, struggles to nap, arches her back, is sick, has terrible reflux, has runny stools, sounds chesty after drinking milk, is very unsettled, wants to be constantly bounced, has terrible (smelly) wind etc. she spends the majority of the day crying. Tried Infacol, Gripe Water, Gaviscon. Currently she's been prescribed Omeperazole to take alongside the Pepti 1 but after a day of difference she went back to experiencing the same symptoms. Went back to the GP two days ago, he doubled the dosage, again, saw a difference for one day and now she's back to square one again with the same symptoms.
I wondered the same thing as you as she's been on Pepti 1 for a while now and she's still so unsettled and the GP said that he thinks Omeperazole can help fix her issues. He agreed that if nothing changes then in 2-3 weeks we'll change her formula to an Amino Acid Formula (I think that's what it's called?!)
In your case I think you should be given AAF because he said the reason he's reluctant to prescribe it straight away is because in his experience children that require AAF formula have terrible skin rashes and eczema. My DD doesn't have this anymore so he said he thinks that Omeperazole alongside the Pepti 1 should help. I'm not too sure about this because after a day we're back at square one, but considering your child has skin related symptoms I believe you qualify for the AAF. Have a look at your local CMPA prescribing guidelines and use these to fight your case. Usually they will suggest the routes that should be taken before it's prescribed and you can show that you've taken the other route. Also, keep a symptom diary daily, this helps argue your case in regards to frequency of symptoms etc.