Can a company punish you for not being able to keep up with work flow by yourself at a one person work location? I am in…

Can a company punish you for not being able to keep up with work flow by yourself at a one person work location? I am in healthcare and I also work alone in my office for a lab company. I am getting to a point where it is getting more challenging to keep up with the work flow on busy days. I want to ask to have a second person staffed here on those days so I don’t fall short of breath and pass out or in general hurt myself. I’m just worried that if I do then they will say no and go after me when I am unable to keep up with work.