Visit to the dentist

I had gone to my dentist about two days ago. I have braces for my teeth so that was why I had to visit the dentist. While the dentist was working with the braces she asked me to rinse my mouth with water.
There was a plastic cup filled with water on a prop in the machine type thing on which dentists usually ask there patients to lie down and then operate on them.
Instinctively I picked up the cup of water and started to rinse my mouth. I did not realize that cup of water may have been used by a previous patient and so did not ask to change the cup and the water for me.
But what if that cup and the water had been used by a previous patient? And since he was there obviously for some dental work there is a good probability that he may have blood in his mouth.
While drinking the water form the cup I did not notice any visible blood on the cup (at least on the side from which I drank the water) or in the water itself.
I do not have any deep cuts in my mouth, i.e. I do not bleed from my mouth but since I have braces there are a few cuts in my mouth.

Also the reason for me suspecting that the cup of water may not have been changed after the previous patient is that on one earlier occasion when I visited the dentist I had noticed a plastic cup of water with some blood on it left by a previous patient, and then I had asked the doctor to replace it.

I know that i am assuming too much and thinking in a very negative manner,but this thing has really started to trouble me. Could you guys please comment on this and suggest what should I do.

Thanks in advance.