I wouldn't put that much weight on that. Most people are super absorbed into their own self (case in point OP, you, don't mean to come off rude just making a point), which is great news because the pressure should be off.

Most likely nobody noticed and you're reading too much into it. If someone asks you, just be blunt and say how it is firmly, don't draw attention to it. It can be something simple as "My throat hurts, just needed some water, BRB" and go get that water because what are they going to do? Give you hard time? It's not high school. You're an adult. Own it. Don't be embarrassed or divert attention away. You can do white lies, "Excuse me, I have bad allergies." End of conversation. I'm in sales and I meet a lot of people, most of them are so stuck in their own world that I have to explain things like I'm talking to a 5 year old. Over and over and over again. Don't mind it man, just live your life. I promise you it's nothing.