The local most of you are thinking of is called Mepivacaine - not "lidocaine without epinephrine".
I am very sensitive to epinephrine and must have Mepivacaine. The only problem, if the dentist isn't careful and gets some of the local in my blood stream it can cause similar side effects to the epi because it causes vasodilation that my body tries to fight by releasing adrenaline. So for some of you, local in the blood stream (harder to avoid on certain teeth) can be an issue, too.
Epi, if given to me doesn't cause that short term of symptoms. Instead it can last for a couple hours (not the numbness, that fades fast) and I feel weird/sick from it for the rest of the day.
I have NCS and suspect POTS. This means I already have nervous system issues that causes problems with blood pressure and heart rate (tachycardia). I also have low blood volume (less blood for drugs and hormones to be released into can mean higher amounts circulating). Luckily a careful dentist, laying me down nearly flat, and a local like Mepivacaine helps prevent the tachycardia.
skbrmom - did your daughter faint right after the shot or while the biopsy was being done? If so it may not have even been the local used. Fainting from shots or while having blood drawn, including the drop in blood pressure, is common and referred to vasovagal syncope - also known as neurocardiogenic syncope (NCS). The drop in blood pressure is one of the key findings for being diagnosed with it. If she ever feels lightheaded when standing in place or dizzy after standing up, please research this.