There are several things to discuss here. First, a 5.9 A1c is far outside the "normal" range, whatever your doctor says. A normal nondiabetic, nonpregnant, nonobese individual will typically have an A1c of 5.0 or, usually, less. An A1c of 5.9 equates to an average blood glucose reading somewhere between 120 and 130, and that is just simply too high, though not severely so. Not yet, anyway.
Full disclosure: personal bias follows. I object strenously to the term "pre-diabetic". IMO there ain't no such thing. Either the body can maintain normal blood sugar without outside help, or it can't. "Pre-diabetic" is like "a little bit pregnant". No such animal. The term pre-diabetic is a useful cop-out for both doctors and insurance companies; it implies that well, this isn't really very serious and we don't need to devote very much of our precious attention to it. But then, they aren't the ones with skin in the game, who must live with the results--are they?
As for insulin, there is a lot of nonsense about it in the popular mind, nearly all of it sourced and fostered by the medical profession. Many--perhaps most--doctors still treat insulin as a "last resort" to be used after everything else has been tried and failed. So of course that's how almost everyone is conditioned to think of it.
Consider the utter absurdity of that. Imagine you had a broken leg, and the doctor said, "Let's just put you on painkillers so it won't bother you." You would probably move at lightspeed to find another doctor who would set the leg in a cast so it could heal, yes?
Insulin is the most powerful weapon against diabetes that exists, by orders of magnitude. Why wait until someone is in such bad shape that nothing else has any possible chance of helping?
If you don't believe that's exactly what happens, consider all the standard stories everyone has heard, e.g., "My aunt was put on insulin and she didn't last a year." Well, duh. By the time she was put on insulin, she was so far gone that it really was the last thing left to do. Here's an idea: how about acting proactively so that the "last resort" is never reached?
The Joslin Diabetes Center in Boston, which is pretty much the gold standard of diabetes care, now puts all newly diagnosed diabetics on insulin right away, even if only temporarily so that control can be reestablished. Presumably they know something.
There are TuDiabetes members (I am one) who finally lost patience with poor control and insisted on insulin for ourselves. It's the smartest choice I ever made.
Finally: as for testing, yes, you should at a minimum be doing it before and 2 hours after each meal. How else can you possibly know how your blood sugar reacts to food? The A1c is a useful guide but it is an average, and an average, by definition, conceals the peaks and valleys (in diabetic terms, lows and spikes). And those are critically important to be aware of if there is to be any chance of fixing what's wrong and establishing good control. You can't attack a problem meaningfully until you know exactly what the problem is.