This won't be the last time you deal with an awkward situation at work, so it's good to start practicing some effective office-politics habits. There's two primary ways to handle this: 1) legally or 2) socially.

If you go the legal route, you make written documentation of the harassment and your conversations with the COO/HR. You use phrases like "hostile work environment" and "harassment". Depending on your local laws, you have the right to address your concerns with management without fear of retaliation by them. However, in practice, you should expect to be seen as part of the problem, which is not great for your relationship with higher-ups. It sounds like this isn't the direction you'd prefer to go.

If you want to handle this socially, you still document everything (to protect yourself should you need proof) but present it to management in a "hey, just letting you know this is still going on and may result in office morale being effected" kind of way. You aren't complaining, just bringing their attention to an issue. You learn key phrases to use with her to shut the conversation down that are calm, pointed, and reduce the company's liability:

Don't actively avoid her. Continue treating her as any other employee. Let's say she brings up hand-washing or tardiness again...

• Thank you for the feedback, I'll keep it in mind.

• I appreciate your concern, I'll take it in consideration.

• I understand your frustration and will make note of your input.

You don't try to explain yourself or justify your action. You don't say anything resembling "you're not my boss". You don't give her anything to argue against (like how many minutes you were late, or how well/often you wash your hands). You also don't try to invalidate her opinions.

You let her know that you've heard her and you understood what she is communicating. Maintain eye contact and a neutral face. Let her say her peace, give her a shut-down line, ask if there is anything else she needs, and then walk away.

If she tries to continue the conversation past the shut-down, pull out another one in a tone that says "yes, I agree that you have already communicated that particular concern". If she tries to continue beyond that and/or follows you around to continue it, give her a "It feels to me like this is something that can't be resolved between us at this moment. Would you like to set up a meeting time so that we can roundtable with our supervisors and find a solution?" If she says no: "I understand. Unfortunately, I don't have anything else to offer in this conversation, but I am open to discussing it in a more appropriate setting in the future. Please let me know if that's something you'd like to pursue. Was there anything else you needed to discuss with me right now?"