If I've had other vaccines or a TB test recently, does that impact my ability to get the COVID-19 vaccine?

The short answer is no. The CDC is recommending that you not get any other vaccines within 14 days of when you get the COVID vaccine. And the reason that they’re making that recommendation is because there are a small number of vaccines that interfere with each other’s ability to provide an effective immune response. There is no evidence that’s the case with the COVID-19 vaccine, but in order to optimize the effectiveness of your vaccine, that’s the recommendation the CDC has made. The CDC’s recommendations are available at https://www.cdc.gov/vaccines/covid-19/info-by-product/clinical-considerations.html