A coworker is making false statements about me to Human Resources

What should I do?

You need to talk with HR - now.

You must explain how these statements are false. You need to ask about this investigation - what you need to do in order to get it concluded quickly, and what are your rights.

And you should talk with HR about how this is affecting your relationship with your coworkers.

Good HR folks are trained to listen and understand. Hopefully this will guide them to a swift conclusion of the investigation - in your favor - and a quick resumption of good relationships with your coworkers.

Do it now - don't wait.

A coworker is making false statements about me to Human Resources

What should I do?

You need to talk with HR - now.

You must explain how these statements are false. You need to ask about this investigation - what you need to do in order to get it concluded quickly, and what are your rights.

And you should talk with HR about how this is affecting your relationship with your coworkers.

Good HR folks are trained to listen and understand. Hopefully this will guide them to a swift conclusion of the investigation - in your favor - and a quick resumption of good relationships with your coworkers.

Do it now - don't wait.

[As @WesleyLong wisely points out - DOCUMENT EVERYTHING. Every communication, every meeting, every hallway conversation. Write it down: When and where, who was there, what was said to you, what you said to them.]