How do I know if I could have anaphylaxis from laser tattoo removal?

Yes, you can most certainly use lasers, and no, you could not have "anaphylaxis" from laser tattoo removal. Anaphylaxis is an allergic reaction to a certain stimulus, referred to as an allergan, for instance, a medication, or a food, or a chemical compound of some sort. Laser tattoo removal simply uses the laser energy to break up the ink in your tattoo into tiny particles, which are then cleared from the body. While you could have a reaction to the laser energy, it would not be anaphylaxis. It would seem most likely that you suffered a cold or flu which was completely unrelated to your laser test patch.