To me, your fasting and HA1c reading. 5.5%, indicates that you are a pre-diabetic, most likely type.2
I suggest that you go search the internet further then conclude your own assesment. To me, most medical practitioners know next to nothing about this horrible malady called Diabetes 2 which is the most painful and costliest known to mankind at this point.
Here are some of the respectable sites: Diabetesdaily.com, Bloodsugar101.com and lastly the famed doctor:DR.Richard Beinrstein authored of Diabetes solutions book.
You asked:Shall I be concerned?
To me, I would, why? Because being pre-diabetic2 , to me, is like being a little pregnant.
and I would stay away from any sugary, soda drinks...and
white rice, pasta, pizza,
I can understand the confusion when a lab has conflicting ranges. Why that is is unknown and only can be answered by the lab. Not all labs, or hospital labs, use the same ranges, in fact most are different from one to the other. Another puzzling fact is I know of labs within the same company that use different ranges. The big question is why doesn't the FDA and AACE [American Association of Clinical Endocrinologist] set stricter guidelines?
As far as your questions, "Which one is to be relied upon? Shall I be concerned at these glucose levels?", the answer to the first is both. Here's why; a fasting glucose test measures at the time of the test, not what it was the day, week or month before. Consider it a snapshot. If you took two fasting tests one minute apart you will get two different results because not all red blood cells [RBCs] are alike. This is why home testing is important.
The A1c is a snapshot for the past 2-3 months, the average lifespan of RBCs. The ADA came up with a formula to convert A1c to eAG [estimated daily Average Glucose]. Your 5.5% equates to an eAG of 111 mg/dl, prediabetes. Basically it is saying for each day over the past 2-3 months your glucose averaged 111 mg/dl. The lab has high range of 6.07% which equates to 128 mg/dl, diabetes. Why so high? Only the lab can answer this.
To answer your second question, yes you need to be concerned. Unless you're willing to make lifestyle changes diabetes awaits you around the corner and that corner is very close. I have written about lifestyle changes - food choices, exercise, weight, lipid panel - in numerous posts. If you wish to learn more about the 'what to do's - not to do's, including home testing times' send me a PM. Good health to you.