Household finance - partner will be on SSP, but the benefits calculator says I'm entitled to nothing. Looking at claim PIP. Anyone been in the same situation?

My partner has head and neck cancer T4B N2C

inoperable currently due to proximity to skull base

he starts chemo Friday so try and shrink it maybe enough for surgery 

he will be on SSP

I have tried the benefits calculator and due to my working 65 plus hours per week 3 jobs entitled to nothing despite increased heating and other associated bills like water double flush because of chemo bed pads and thermometers and milkshakes etc 

seems like hep is for people who get benefits already and really being penalised for working so hard now my income has to cover two. No hep on council tax or water etc

looking at claiming pip

anyone else same situation that can advise 

stressful enough without finding extra money to cover cost

I am not even in forty percent tax so so not have enough income To cover two despite what the benefits calculation says

thanks