Fred99:Not disagreeing - but if I was the OP I'd take the meds as the Dr suggests and to hell with it - it's a one-off phobia (needles) not more general / constant anxiety.
They work - brilliantly. Enjoyably too - which has the potential to be a problem if you (think you) need them all the time.
It's a belt-and-suspenders thing, presumably the meds will be a very mild benzodiazepine because they can't risk sedating you to the point where you can't safely drive or whatever. So yes, definitely take the meds, but they're usually used as a complement to other anxiety-management techniques, with the two reinforcing each other.