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Good to know that you are careful with healthcare. Firstly I would like to know what was the reason to take a TT injection? On a general note, the injection needle scenario you described is completely safe from most serious viral infections, but only a few bacteria may persist. You see, any organism that develops disease inside a human body grows in a warm medium such as blood and requires a liquid temperature controlled viable environment. But in this case, the bedsheet is a nonviable environment for any infective organism or germ. Hence the chances of you falling sick from that needle are as low as finding a shooting star in the sky. Although I do not say it was completely sterile, it may cause at most a slight immune response that may look and behave like a mosquito bite. Keep me updated with any suspicious symptoms you notice and do not worry, we are here for you. The nurse was not wrong either. Take care.
Using a rubbing alcohol dipped in cotton over your skin prior to the injection makes your skin sterile and also the needle as it goes in.Regarding follow up:
Follow up as necessary.