Am I legally required to stay and work?

Who told you that the place would shut down for 14 days if an employee tested positive - your impression?  If you heard that from some nobody who was just mouthing off, then it means nothing.  If you were told by the employer at the interview or since, then that's different, but you will have to prove that that is their policy and you don't have it in writing, do you?  If you wore a mask, which you should be wearing - and social distancing, then your risk would be less, and if the other person was wearing a mask.  If you decided to have her in your car, then you took on the risk.  You can't blame your employer for your stupidity.  If you were both wearing masks, then you still took on the risk, but it was a smaller risk.  Still, any risk is too high a risk for me.  But not for you.  Now, you decide you want to stay home from work, be paid for not working, and you have come up with some lame reason why you should be entitled to do that.  Wear a mask and social distance and stay away from your mother for 14 days, to make sure you did not contract covid.

look for a hotline for your state to report businesses not following covid regs...and report your office....if they are legally required to shut down, they will be closed....i don't know about you getting paid though

You are not legally required to work. But they are not legally required to pay you if you are not there. The exception would be if you have the virus and can prove you contracted it at work. 

And the exposure to the patients?  I think your question is why we have not been to an optometrist since covid started.  Putting your face and eyes into that machine which has to have a lot of covid germs because it cannot be cleaned.  Cleaning it for germs would ruin the machine.  Plus, the optometrist is marginal in the world of healthcare, as the manager has indicated.  What you should do is find out what the current health rules are and use them to guide your decision. Call the health department.   Find out how your friend is doing.  Is she sick and a second test.  3rdly, ask your manager about the issue.

So quit and go home, if it bothers you.  Then file a workplace complaint.

If you want to keep your job, you are legally required to stay and work.  If you were wearing a mask and doing all the things you should be doing to protect yourself, then you ought to probably be fine.  Get tested if you like.  If she is positive, you likely are already positive if you are going to be.  

1) What you were "under the impression" of has nothing to do what the policy really was; 2) the employer gets to make the rules and if you don't like them you are free to work somewhere else.