Am I meant to be claiming disability premiums? How? Would being on higher rate PIP change this?

Is your ESA the old ESA or is it new style ESA?
If new style ESA you cannot get these premiums.
If it is the old form of ESA this can include the premiums if you have an income based entitlement - whether or not this is possible would depend on why you are currently restricted to contribution based ESA. If it is due to savings over £16,000 then income based ESA is not possible, If it is due to other income then it might be possible that you have some income based entitlement if the premiums are applied.
An increase to your PIP award would not change any of the above.

missybpink said:

Hi its old style but my husband works so they put me on contribution based.

If you live with your husband you are not entitled to a Severe Disability Premium unless he also gets a disability benefit.
Your ESA will be calculated by first working out your income based entitlement which will include the enhanced disability premium (the disability premium does not apply to ESA). There will then be a deduction for your husband's earnings and any other relevant income/savings. If the income based ESA entitlement remaining is less than your contribution based entitlement you just get paid the contribution based amount (as in your case).