No risk In medical facilities needles are always brand new
You are in a state of anxiety right now and so your fear of HIV is ruling your head and you and not looking at this logically, you will not get HIV from a testing centre.
Using the same needle on your own arms of course is not a risk, when you say that you touched the openin I assume you mean where the needle went in? It would be IMPOSSIBLE to get HIV in this way, absolutely impossible.
To ask if nPEP is warranted is totally over the top. NO you do not need nPEP and no you will not get HIV in this way.
i agree with zam zam your anxiety is making you think unrationaly. there is no way you have gotten HIV that way. and HIV is inactive in air. so you can't catch it in this way.