I have read that this loss of smell and taste is definitely commonly reported as an early symptom. This virus has a lot involved with it. This is an easy one to spot.
As AnxiousNoMore says, other viruses can have this effect as well, not just Covid-19. From another website: "Up to 40 percent of people with other viral infections, such as influenza or the common cold, experience a temporary loss of smell that usually reverses itself in a couple weeks. The condition is also common among people with allergies." I have also read anecdotal reports that suggest people who have loss of smell and taste are not the ones who get the most ill with Covid-19 even if it is Covid-19, but when I tried to find the source of that comment just now, I couldn't locate it, so it might just be a story.
Anyway, everything said, do see if you can get tested for Covid-19, but try not to scare yourself to pieces. A lot of times, even people with positive test results are just sent home to take care of themselves there.
Possibly but there are other reasons you can lose these senses. Have you called the local health authorities to see if you can test?