You are over protective.
Don't act like that.
Every medico person use disposible niddle and syringe every time so don't worry about it.
Medicine world maximum keep sterilization to patient. So there is minimum chance to infection for any kind of disease.
At this age this type of thinking are normally seen but don't worry your are completely safe.
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Health Tips
Take proper healthy food adiquate sleep and always be stress free and always be happy.