It sure looks like Elaeagnus species to me too. There are apparently two species of Elaeagnus present in Florida and both are up in your part of the state. Your plant looks most like E. umbellata to me but both are listed as Category II non-native invasive species in Florida. Here are our database entries: Autumn Olive (Elaeagnus umbellata) Silverthorn (Elaeagnus pungens)
Hmmm so I should probably pull that sucker up and get rid of it? Thought if a good gift from unknown sources I would put it somewhere else but sure don't need an invasive that could put a hurting on me!
Each cloud has a silver lineing if only you look for it.