When the nurse at my GP surgery takes bloods, they get sent to the public hospital. The results get sent back to my GP, but I think the public hospital still have all the records too. I am able to get a full copy of the results from my GP if I wish. I do have to pay €30 for the nurses fee. It would be free if I went to the public hospital with a form. But I'm happy to pay for the convenience.
You should be able to bring the blood results to the consultant yourself. I used to do this. The consultant filled out a form so it was clear which tests needed to be done. Then the nurse at the GP practice did the rest.
It is not unusual for patients to have their own test results. My son brings a disc with his recent MRI scan from the Radiology Dept in one clinic, to the Orthopaedic Consultant at another clinic.
(As I'm sure you're already aware - you need to ensure the right tests are done, and to know whether to fast or not! But if the nurse is taking blood anyway, it's just as easy to fill 4 vials as 1, once she uses the correct containers and forms)