OP you may be entitled to claim rent supplement if you are now working less than 30 hours per week, but as gippiman pointed out the value of your property etc will would be assessed as means.
Also health boards set a maximum rent level for each area. This means that if your actual rent is above this level, you will only get rent supplement based on the local maximum set by the health board. If your actual rent is significantly higher than the local maximum, you may be refused rent supplement altogether.
Your partner might now qualify for a social welfare payment, so he should check this out also.
You may also qualify for some sort of family income supplement, especially since you have a child, which again you could look into.
With regards to the property that you own with your brother, you could consider asking your mortgage provider to switch you onto an interest only option, for a set period or until such a time that your financial situation improves.
I would suggest that you pay a visit to your local Citizen’s Advice Centre, who would be able to advise you what exactly you may be entitled to claim for. Your local Community Welfare Officer would also be able to advise you on what options are available to you.
Meanwhile, you should make an appointment with your local MABS office
www.mabs.ie who would be able to advise you on any other debts that you may have & are running into trouble with.