The lady at reception is coughing at my work.. ?

Speak up instating of wasting company time on YA. Ask the receptionist if she is felling okay.  Ask her if she'd please wear a mask at her desk since she is coughing.  Talk to your boss about working from home. Talk to HR about installing a Plexiglas shield in front of the receptionist.  Wear your own mask when you walk by her.

The reality is that you can't get COVID-19 from people who don't have COVID-19.  There are dozens of things that cause people to cough, including seasonal allergies.  You aren't likely to catch anything from someone you walk past.

You can decrease your chance of bringing home germs on your hair and clothing by taking off everything immediately,  putting your clothes in the washer and taking a shower before you enter your mother's space.

I would think in today's environment you have a case to ask HR to have the person tested.  You can make the case that the cough is causing some anxiety which effect productivity so it is to the company's benefit to demand that person be tested.  I would do so in writing.  I might also ask the person if they are ok and suggest that they wear a mask until they can get medical attention to stop the cough.  When you do that note the time and date and notify HR that you did so just in case the person in question tries to bend it into harassment.  Beyond that I don't know what else you can do.  A healthy person has a right to work.