As noted above, the vaccine cannot give you COVID-19. However, the vaccine takes two weeks to work, and a few people in the U.S. have gotten COVID-19 around the same time they got a vaccine. Some COVID-19 symptoms that are not vaccine side effects include cough, runny nose, and loss of taste and smell. Please refer to the CDC guidance here on what symptoms are more likely to be from COVID-19 illness.
Remember, you should call your provider if you experience severe headache, abdominal pain, leg pain or shortness of breath within three weeks of getting the J&J vaccine. These may be signs of the rare but serious blood clots that occurred in a small number of people who received the J&J vaccine.