I've responded to similar posts previously (some posted at the end of my response here) but yours warrants some further commentary. Generally everything your practitioner said is technically correct - yes sometimes the needles can hurt and for the most part this dissipates with a few days and may only happen a time or two. Instead of talking it away, however, your practitioner could simply use different needles and/or different techniques to avoid this. Generally the technique is to blame. The point she used, PC 6, -can- cause nerve damage if needled inappropriately and it is somewhat disturbing that she wouldn't be aware of this. My guess is that she is, but was simply trying to appease you in your concern.
One of the many things which separates fully trained licensed acupuncturists from MD's, DC's, etc. that practice acupuncture is the extent of our training which culminates in better technique, better point location and generally a better understanding of the underlying anatomy.
Some practitioners use more aggressive/deeper needling techniques or do not properly account for differences in anatomy (i.e. size of wrist, etc.) well. There was actually a study a while back done on needling of PC 6 in particular (I tried but couldn't find it right now...). The study found that 20% of Chinese practitioners studied (it was a small study - 20 or so practitioners if I remember correctly) caused nerve damage to the point with more aggressive techniques. It was unclear whether or not this lead to any permanent damage. My understanding is that permanent nerve damage is extremely unlikely without the most invasive and improper of techniques being applied. A similar study looking at a few points in the neck illustrates some of the possible dangers of not being trained well (see "Clinical anatomy study on the acupuncture safety of tiantu (CV 22) and qishe (ST 11)").
So the short of this is if your practitioner really did say - "since the needle was so small and thin there is no way it hit a nerve" - this is 100% incorrect. Chances are very, very small with proper technique, but it can happen with improper/aggressive technique.
I would venture to say that you will be fine after a few days and that this will more than likely never happen again. I would say, however, that a practitioner that lets a patient dictate how many needles to use because of fear is generally a little uncomfortable with their technique to begin with. Proper technique would mean you would feel very little from the needles, even if you are stressed or apprehensive the first time (which, by the way, many people are). In fact, proper point selection and technique should make the treatment a very enjoyable, relaxing experience. If this is not the case for you I would simply find another practitioner.
My general recommendation would be to voice your concern, go back for another treatment or two, and if this response continues and, more importantly, you are not improving with your main complaint - find someone else.
Related Responses - "Pain with Needles", "Back Pain Worse After Treatment"