The black light you have is a long wave type, it's not going to harm anything. if it was a medium or short wave black light then you would have problems. The amount of radiation coming from your light isn't enough to do anything.
Following is taken from a website:
A long wave UV-A black light is the type used for entertainment purposes, such as at concerts and in clubs. It makes materials glow and creates atmosphere.
A black light that emits medium wave UV-B rays causes certain bodily fluids to luminesce. Crime scene investigators and forensic labs use these to detect blood, saliva, semen and other fluids. Medium wave black lights are also used to detect anti-counterfeit markers in currency and have many other security applications.
A short wave UV-C black light emits radiation that is destructive enough to purify water of living contaminants and to sterilize medical equipment. It has a variety of industrial uses and is considered “germicidal.”
Because of the potential harm to the eyes from unseen radiation, one should not stare into a black light. Professionals who work with black lights, particularly UV-B and UV-C lights, wear UV-protective eyewear with yellow-tinted lenses. The yellow tint blocks blue light waves in the HEV or near-UV spectrum, which doctors have associated with macular degeneration. Barring staring into a black light, experts do not believe that occasional exposure to black lights as used for entertainment purposes is harmful. However, those with prolonged or repeated exposure to black light should wear UV-protective eyewear that includes HEV protection.