I respect that you have been educated enough to recognise that it is of great value to use licensed technicians and estheticians for your body art. Techniques employed by the artist should include "aseptic technique" which is a means of creating an environment that reduces the risks of infection. The licensed provider has been specially trained to know how to do so. The use of a new needle is a critical component, as well as proper cleaning or sterilization of other associated equipment. Equally important is hand washing and the ink supply itself. You have not indicated if the tattoo site is reddened or hot to touch, if the needle site is oozing at all, or if you are having a fever, or increased pain at the site.. These are all possible indicators of a localized infection. Nausea that passes on its own (that you state seems triggered by your thinking about the possibility of infection) is not typically linked to a skin related infection - in the absence of other signs. If any of these signs manifest, I would ask my primary physician or a local urgent care center to evaluate you and make appropriate recommendations. If your friend is a good artist - I would also recommend that you strongly suggest they get a license so that they may continue to practice their art safely, for his/herself - and for the client.
Wishing you the best of health!