Other people can probably answer better if they've dealt with severe nappy rash, but I know people have mention just patting dry and not rubbing the sore area with a wipe.
With the wool the thickness won't make that much difference, the wool will still be breathable. He could react or be allergic to either wool or lanolin, but it may not be either. You'd be able to tell pretty easily with the lanolin by doing a test spot on his skin, so try rubbing a little bit in to the back of his hand on his leg or somewhere where the skin is thicker. It could be a reaction to washing powder too, but then if he's been fine before... If it stays bad into next week or gets worse, I would go back to the doctor quickly and see what else they can suggest. When Ella has had bad skin, the only thing that worked is prescription creams, but that's been eczema on her legs and face, never on her bum. Her bum and legs have always been better in wool. Lanolin is actually really good for healing skin (provided there is no allergy to it). That's why you get medical grade versions of it. We have changed Ella more frequently when she has any sort of rash, but nappy free time really helps too. We use metanium and think it is brilliant stuff but a lot of people can't stand it. It tends to dry the skin out though, wheras you probably want something like bepanthem or kalmison.
Able to replenish the lipid bilayers, lanolin can be used to maintain and repair the skin's natural barrier, whilst protecting it against damaging environmental factors. Whilst lanolin is able to protect the skin by helping to maintain a healthy skin barrier function, it also possesses natural anti-microbial properties that provide additional protection benefits.
It's quite possible to have ezcema and be allergic to animal fibres so react to wool (allergic to sheep basically). I have asthma and allergic to cats or dogs. Ella has a touch of ezcema though no allergies yet. We used Oilatum and GP prescribed a big bottle of bath stuff and of cream for Ella as it's expensive over the counter. It's great, but sometimes we need to use medicated cream. There's the same patch appearing flaring up on Ella's face beside her ear atm.