The real issue here is whether or not your parents need help with daily living, washing, bathing, food prep., cooking, shopping etc.?
If they do, then they are classed as disabled, as such they each, individually, qualify for a disability benefit, Attendance Allowance, if they are over 65.
If either of them has dementia, then that person is exempt from Council Tax.
If caring for them has a significant effect on your life, then yes, you ARE a carer.
Have your parents had a Needs Assessment from Social Services?
Have you had a Carer Assessment from Social Services?
Have you sorted out Power of Attorney?