Overpayment of housing benefit and council tax benefit?

Can anyone help please? I am a student who has declared all my income, which consists of student loans and i am also a carer for my disabled child who is 20 years old. At the start of my academic year i recieved a letter from the council saying that i do not have to pay rent or council tax. In may i then received a letter saying that i had been overpaid by �400 housing benefit and �126 in council tax. These letters are not very straightforward, so i appealed saying that i do not think that i should have to pay this as it was a fault of the council, they replyed saying that it is a recoverable amount and that i should of checked my letters to see if everything was right. The mistake that they made was that they did not include my carers allowance in their calculations. However i did declare all my income. My argument is that i do not know how to calculate how benefits are paid as this is not my job and there is also nothing in the letters which tell you how to actually work out what i am entitled too. I was sent three different letters at the time i put in for these benefits and not one of them contained the carers allowance entitlement. I umed that as i had declared it and it was not in the letter that it was not means tested. Can anyone help with regards to the law concerning this please, and if it is possible that i could actually put anything to the tribunal in order to try and win my case? I appreciate any help that you could give. Thank you