You are in luck, I have been asked to look at this for a relative who is approaching 70 and gets a UK pension. Can I just say on first reading the guidelines I can only say holy s.... smoke. I am not surprised you are bamboozled.
Here is the bit about EU/
EU/EEA entitlement
Under EU Regulation 1408/71 a person moving from one EU Member State to another retain the rights and advantages acquired through social insurance contributions which include access to health services.
EU pensioners resident in Ireland who are in receipt of a qualifying pension, as evidenced by form E121, are entitled to a Medical Card provided they are not subject to Irish social security legislation.
Pensioners from the UK must provide proof that they are in receipt of a UK social security pension. The UK social security pension is the only qualifying UK pension for
entitlement under EU legislation.
Any additional income to the qualifying pension not subject to PRSI is not taken into account when determining entitlement to a Medical Card (e.g. Occupational Pension, Investment Income etc.)
Dependants resident in Ireland of pensioners with entitlement under EU legislation are entitled to a Medical Card on production of a form E121 provided they (the dependants) are not subject to Irish social security legislation. "
Reading the above it would appear you can apply but there is this bit " provided they are not subject to Irish social security legislation." Now at the moment that has me baffled. In your case as you are in receipt of a carers allowance it may mean you are subject to " Irish social security legislation." It states you wont be means tested so that figure of €298 does not apply. And the €298.00 is per person but... it is very badly written and it is still dated 2009.!!! I'd give them a ring or call in that 1890 is dear I think.
If you have any questions before you send off this form, please phone Callsave 1890 252 919 or
call to your Local Health Office.
use this no instead and see if you can get through 018647100,