Hi F., My son went through a similar thing at that age so I know how frustrating it must be for you! He went from eating great and being a really happy baby to crying all the time and eating less... The most important thing is to talk to your doctor. Every baby is different and there can be a number of different causes. My son was diagnosed with acid reflux and was put on medication. I drank a lot of milk, and my doctor said that one of the milk proteins was prob. causing it. I started drinking rice milk (I think soy is gross) and kept breastfeeding and pretty soon my son grew out of it and stoped needing medicine. (he's a year old and recently started drinking cow's milk too and he's been fine)I've also heard that some baby's get a similar sensitivity to wheat, so your Dr might mention that.
As for the eating for 4 min on one side... I asked my nurse about that when my son started that too. She just said that as time goes on, baby becomes more of a "PRO" at eating and can drain the breast faster than before. Don't worry about baby not getting enough to eat as long as he's not losing weight. Also your milk production will keep up with him (that whole supply/demand thing) When my son stopped nursing on both sides, I would feed him on one side, pump the other side so I wasn't sore, and the next time switch what side he ate from. (a good way to build up an extra milk supply in the freezer too)
Eczema can be caused by several things including heredity, and outside irritants, and changing diet can sometimes help in babies, but is usually a last resort. You should go on this website, they have a lot of info on it... http://www.eczema.org/faqfile.htm
As for the diet thing, babies under 6 months old can't yet digest foods properly and feeding them certain foods at a young age can actually CAUSE food allergies. (don't freak out though, cuz it usually takes a little time for this to happen, so if you gave baby that stuff once you prob didn't cause any harm) On the flip side, if a baby shows signs of a food allergy, and you stop feeding them that food... then they usually grow out of it as their digestive system develops more (meaning baby might be able to eat apples and pineapple later down the road)