What state are you living in? Please explain "job seekers allowance", "care allowance" and "income support" as they are used in your state, or were you referring to something federal? Do you have any source of unearned income? Does your dad receive either Social Security or disability income? Does he own his home and do you live with him or not? Does he have any unusual assets?
Any other detailed information could lead to answers that may be of help to you.
Are you trying to claim unemployment benefits while seeking work because you are unemployed? In CA, a job seeker must be available for a suitable full-time job with some exceptions. If the State of CA disputes benefits of your claims, you then have twenty-one days to appeal the state for just cause instead of falsely claimed benefits. You must provide supporting documents that are consistent with your dad's caregiving situation. Does your dad pay more than 50% of the household bills so that he can claim you as a dependent? It is really hard to figure who is trying to support who in a household under a "domestic" working situation such as your caregiving role to your dad.
I'd like to help, but I would need more details first. I'm assuming the reason you don't qualify for care allowance is because your dad's income is too high? If your dad's gross taxable income (excluding social security) is more than half his support (his half of rent, utilities, clothing, food, etc), than you won't be able to claim him as a dependent on your tax return either. My advice is to consult a professional. Bring your facts & figures to your meeting, or have them at the ready when emailing or calling. It will save you time & money. Let them tell you where you stand.
Any other detailed information could lead to answers that may be of help to you.