The fabric conditioner compartment not emptying means your jets are blocked.
Take the drawer out, dismantle it and wash in hot soapy water. I use a bottle brush as it can get in the nooks and crannies.
Now clean the drawer cavity - go back as far as you can. The bottle brush is good here too. Feel along the top of the cavity for the jets - clean this as best as you can. I use a strong plastic toothpick.
My guess is though that your washing powder is not up to the job. It's difficult when you have excema - try washing at a higher temperature.