It's not PIP for a child, OP, it's still DLA. It's very hard to get DLA for a baby, as all babies require round the clock care. If you have to give her medication or carry out any therapeutic stuff for her, make sure you mention it. Basically, you have to establish that she needs significantly more care than a baby of the same age without health problems. Submit as much medical evidence as you can, eg hospital letters, copies of prescriptions etc.
If you manage to get DLA for her, your UC will go up by £128 a month (disable child element), plus you will be entitled to have the carer's element (£160 pcm) added to your UC, which will help.
It may also be worth considering if you might be entitled to PIP because of your own health problems. If you have a decent advice centre or CAB in your area, give them a call and they should be able to advise you if an application is likely to be successful. (I should stress, this won't be quick: the DWP seem to be turning down every PIP applicant who's not actually in a coma atm, and we're having to take almost every case to appeal, which takes approx a year). Well worth doing though.
And please, please, take a look at your outgoings and see what you can do without, eg expensive phone contracts, Sky/Netflix, switch your utilities to cheaper providers. And see if you're entitled to a reduction in council tax.