Lol nothing to worry sir. It wont be something that serious. Maybe a bit cold or cough. but nothing to worry about. It won't matter if you take a mild medicine for cold though.
I agree with the above post. Never hesitate to speak up when you are concerned in a medical setting. She may have done it without even thinking, and needed a reminder. But I'm sure you're fine.
Sinus infections have many causes, and you don't know the cause of hers. But the likelihood of you getting it from her touching your arm and drawing your blood are pretty much nil. If someone ever makes you feel uncomfortable in the healthcare setting, you have every right to say something. They won't take it personally, if it is done in a tactful manner. It may just open their eyes and make them more careful in the future.