Chronically overtired 3.5 month old please help!

[cheerfullysleepless]

Am beyond stuck!!! Gorgeous baby boy has eczema and some reflux, both being treated but not cured and woke him up quite a bit in the night. The eczema is new and bad and he has been waking him up (think so anyway as he's scratching etc even with mittens on) every one to two hours at night and now just seems so overtired can't settle for proper naps in day. Never been great at napping but even car and sling or feeding to sleep failing now and maxing 40 mins, often 20 sometimes 10. The last few days he's had at least three hours sleep less than normal and so unhappy, cries far more often and longer and at things he used to grin at like blowing raspberries on his tummy (made him howl for two hrs thus morning) or looking in the mirror etc and really stopped being interactive at all just stressed and squealy. Feel so so sorry for him and no idea what to do please help !!!