Hi, from what I can make out, you were refused ESA and are now getting the assessment rate while you await appeal, is that correct? If you think that you should get income-related ESA, you should ask for an ESA3 form to fill in, this will take details of your income and assets and allow you to get IR ESA if entitled. I don't think that this form can be downloaded or completed online.
Asset rule for ESA(IR)