ESA Daughter - months without any money

Hi,
sorry if this is repeated somewhere but I’m tired of searching the Internet for a straight answer. My Daughter was thrown out of university- for want of a better phrase- due to having depression since landing there and struggling. Moved to Kent to live with myself and my Husband - claimed ESA March 15th assesses May 9th - put in the support group - has not received a penny to date ! Rang countless times and last week I was informed we had claimed contributions based instead of income - I dispute this as I know she hasn’t made any contributions to qualify ! So told no award letter as no money due - another form sent last week to us to complete - again - to claim income based !! I’m at my wits end as my Daughter has received not a penny since March 15th - Is this usual? Is she entitled to income based as living at home we’re both myself and her step father work? I do hope so, as she is classed unfit for work for the next 12 months - surely they should have known which type of ESA she needed due to finishing University!? I feel they have messed up and passing the blame onto us - I doubt they have a full scanned claim form in front of them to show me my ‘error’ !?? Thank you in advance