Strictly speaking, you should automatically be a public patient. Being a private patient is something you opt into. However, if you told your GP you have health insurance, s/he may have assumed you wished to go privately and booked the tests accordingly.
As Staples says, you GP should be able to re-arrange the appointment if you're not already going publicly.
BTW, if you're a PAYE worker, you can get tax relief at the standard rate for certain health expenese. So if you do choose to go privately for the tests, you can make a claim to Revenue for any costs that aren't covered by your health insurance.