Yup Ushuffle, Luvox interferes with caffeine metabolism so your morning coffee hangs around your body for much longer than usual. There was anecdotal evidence ("user reports") of this for a long time, until a specific study proved it a couple of years ago.
Uhmm.... I hate to be blunt. Is your prescribing doctor a psychiatrist? I'm just wondering because his/her choice of meds seems unusual; Wellbutrin and high doses of Effexor are not 1st line choices for the treatment of anxiety. And neither is Luvox . There is this myth floating around that all SSRIs are basically equal. They are not. While they belong in the same family from a chemical point of view, their effects are different in the short and long term.
Luvox is usually prescribed to treat OCD - despite being considered the most sedating SSRI. Paroxetine (Paxil), citalopram (Celexa), escitalopram (Lexapro) are the *usual* choices used to treat anxiety - that doesn't exclude the possibility that Luvox might help. We are all different and the only way to know what med fits is by trial and error. For example, Wellbutrin *really* helped my anxiety - maybe because my anxiety/panic is secondary to depression.
Good luck 
edit: here's the link to the study that shows Luvox-caffeine interactions:
Fluvoxamine impairs single-dose caffeine clearance...[Br J Clin Pharmacol. 2005] - PubMed Result
Simply put, caffeine lingers in your body for longer than usual. Ask your doc about lowering your caffeine intake.