Council housing

Hello Friends!
This is my first post.
I first try to explain the situation.
Me, my partner  are in U.K. more than 5 years, we have a 2 y/o doughter. We are now living in a one bedroom apartment.
My partner had some big issues during pregnancy and the diagnosis was ulcerative colitis and latent TB
Ulcerative colitis therapy has lot of consequences like osteopenia, overweight-obese, fatigue, headache, insomnia, she is immunocompromised and have limited capability to work.
Lets talk about the apartment.
There is no extractor fan in the kitchen (landlord refused to install one, not required by law), the window handle is not easy to reach so to open the window  is difficult especially for my partner because there's a counter in between and she has limited capability of movement. Also because of the counter it is not possible to open it widely.
This conditon leads to have condense in the house  and mold is  growing easily on walls and ceiling, in the kitchen (ceiling, walls, cupboards, behind cupboards and washing machine)  bathroom (ceiling, walls, underneath sink) and bedroom.  It is well know that this could worsen her health condition but also our child's and mine.
It is also difficult to find another flat due to low income (I work 30 hours and I need to help her taking care of house and child) and having a baby.
Electricity bills for this apartment are very high, the Energy Performance Certificate figures £2421 over 3 years  but we spent £2134,9 from 18/7/2017 to 28/11/2108 and still the bills are very high, we're paying nearly double of what figured on EPC.
I applied for a council house main reason was: "overcrowded" and they automatically assigned us priority band 5. In order to try to get a better priority code I changed the main reason in "Property unsuitable on age or health grounds"
They didn't assign us a new priority band.
Now my question is:
what is the best I could do to apply for a council house? Any suggestion is very welcome!
Thanks all