Ask Mr. Smarty Plants

That is intriguing!   I don't know of any flower that naturally glows in the dark in New Hampshire.  Apparently, someone has figured out a way to make any flower glow using chemicals or with solar-powered fiber optics and are working on genetically modifying them to glow by adding jellyfish genes (google "flowers that glow at night"). 

So, I have a few questions/suggestions:

1. You didn't say what kind of tree the glowing object was in.  Was it, perhaps, a Liriodendron tulipifera (Tulip tree)?  I know our database doesn't show New Hampshire as part of this tree's distribution, but I know they grow in neighboring Vermont.  A late-blooming flower on one of them would probably show up with a pale glow in moonlight.  However, the moonlight would have been pretty meager last night according to the Moon Phases Calendar.
2. Could it have been one of those helium-filled balloons bought to celebrate someone's birthday or other special occasion that got caught in your tree?
3. Have you gone out with a pair of binoculars in the daylight and tried to find the "flower"?   If it's a night-blooming flower, it probably isn't going to be very easy to find.  It would be worth the look, however.
4. If it wasn't the tree itself blooming, then I think it would have to be a vine.  Check around the base of the trunk of the tree to see if you can find a vine that is growing up the tree or perhaps a vine growing over to that tree from an adjacent tree.  Here are some candidate native vines that could climb in trees and are known to grow in Rockingham County, New Hampshire:  Humulus lupulus (Common hop), Clematis occidentalis (Western blue virginsbower), Clematis virginiana (Devil's darning needles).  There are two other non-native vines that grow in New Hampshire but haven't been reported in Rockingham County, but do occur in neighboring Strafford County.  They both have purple flowers:  Ipomoea hederacea (Ivyleaf morningglory) and Ipomoea purpurea (Tall morningglory).
5. There are fungi that emit phosphorescent light (e.g., foxfire).  Usually the light is yellow green, but there have been reports of reddish lights.  One species, Panellus stipticus (Bitter oyster), occurs in the New England area and can be lumiscent, but its glow is greenish.
6. Then there are the glow worms (actually not worms, but larvae of a beetle in the Family Phengodidae).  Some species in this family occur in the New England and as far north as southern Canada.  Some Phrixothrix species larvae glow yellowish on the body and red on the head, although I think this species is limited to South America.
7. Maybe someone tossed a glow stick or light stick or glow string or some other glowing material up and it got caught in the tree?

This pretty well exhausts my ideas about what you could have seen in your tree.  If you have already solved the mystery, please let us know what you discovered it was.