Can you get a reaction to the tetracaine?

Possibly: Tetracaine falls into the "ester" class of local anesthetics, and, unlike the "amide" class of such, may cause an allergic reaction, albeit very rare. It is long acting, meaning numbness and inability to move affected area may be quite prolonged(several hours). If given improperly into a vein, it can cause cardiac arrest and/or seizures but this is also rare, if administered properly.

Allergic compound: You could although very rare. Most of allergies (starting with pruritus (itching) and ending with severe life threatening condition are because the esters during the metabolism (breaking down process) form PABA (para-amino-benzoic-acid) which is responsible for most of reactions. The amide type of local anesthetics also can produce allergic reaction but not so frequent