Relationship between hemoglobin value and glycoslated hemoglobin value

Patient: Is there a relationship between a person’s hemoglobin level and an A1C? I had my annual check up and my FBS was 103 and my A1C was 5.7. Per the lab both are considered high and my Dr. wants me to lower both, FBS less than 99, A1C less than 5.7. I noted my H and H is 15 and 44.5 , which is higher than most people. Since the A1C is measuring the glycoslated hemoglobin, would the A1C be elevated as there is more hemoglobin? I am concerned as my paternal grandmother developed TypeII Diabetes. I am a 64yo female and want to avoid it if possible.