It sounds like this manager is creating a difficult situation for you but until she takes adverse action against you there may not be much more you can do except to continue what you are doing and be vigilant.
You may want to be sure that HR is aware of what is going on- particularly her asking who made negative remarks in the event there is any retaliation.
This is my opinion and should not be construed as legal advise for your specific case as there are many more facts which you have not provided.
"Hostile work environment" doesn't mean what most people think it means. It doesn't mean that your supervisor is being hostile, or creating an unbearable workplace with obnoxious or rude behavior. Supervisors are entitled to act that way, and there's nothing illegal about it. It may be bad business, and it may be unacceptable to reasonable people, but it's not illegal.
The only time a supervisor creates a "hostile work environment" in a legal sense is it's based on what we call a "protected characteristic:" race, age, sex, religion, disability, and a number of others.
Here, you have some indicators that what the supervisor is doing is based on your sex. There is, however, more to the story.
To be illegal, a "hostile work environment" based on sex must be so severe or pervasive that it fundamentally alters the nature of the workplace. Usually, a few comments based on sex or an accusation of wrongdoing won't be enough.
If you feel that your work environment nonetheless qualifies as a hostile work environment based on sex, gather all of the incidents that would indicate that, and analyze them as a whole. If you decide to take action, make sure to do so within your statute of limitations, or your right to do so may disappear forever.
I hope you can resolve this issue. Good luck.
Craig T. Byrnes
Disclaimer: Please be aware that I am not offering legal advice, nor forming an attorney-client relationship with you. I am not representing you, nor doing anything to protect your legal rights. If you believe that you have suffered a legal wrong, take action before any statute or limitations expires, or your right to do so may be lost forever. Good luck in your legal matter.