Dear Ellee,

Looking at your baby's symptoms it seems very likely that your baby has inherited some of your tendencies towards cows milk allergy/intolerance and eczema and asthma. Your baby is showing many symptoms of an immune system under stress. There is a very high correlation between cows milk protein allergy and reflux, cows milk allergy and cradle cap and eczema and asthma.
The immune system can take a certain amount of stress - but when there is too much stress - symptoms develop. This could explain why your baby's eczema clears up when you go away. He may have other allergies or intolerances to something in the environment. When he is no longer exposed to that, his immune system can cope again and the symptoms go away.
You know how you feel when you are sick with bronchial asthma? You probably just want to "hang out", want small frequent feeds, and "need a cuddle"? Eczema makes him feel "itchy and scratchy" - completly out of sorts. This is probably how your baby is feeling much of the time. Your breastfeeding is "holding him together" outwardly. But he is just not at ease with himself - having his mum close is the one thing that helps him feel good.
Many mothers find it helpful to go on a dairy free diet. You may seek the assistance of a dietician to ensure that you have enough to eat. You need to be a "label decoder" and cut out milk products including casein and whey in even non dairy margarines, baked goods and processed foods.
Babies like this are high needs - it's tough going. In your case, formula is likely to excacerbate the problems. Formula is, after all, cows milk. Have a read of the book I suggested earlier - well worth it.
You may also consider getting your baby a check up by a pediatric chiropractor or osteopath. This may allow your baby to feed more easily and assist with digestion.
Good luck - you are doing a great job under difficult circumstances.