Stitches after fainting: Will my eyebrow hair grow back?

In general hairs may not grow back on the scar.  You may need to wait for the wound to completely heal to determine how it may look.

If you are left with scar tissue it is unlikely that hair will grow back in this direct area. However, It is possible to get a small eyebrow hair transplant to cover this up later if that is the case. With such a small amount of stitches though, it unlikely that you will have any significant scarring. 

I gather that you had an eyebrow laceration and had it sutured closed. Hopefully the edges approximated well, If not, you may have a scar and some lost eyebrow hair which can be  tattooed or transplanted.