Washing your hands properly seems to be the best working solution. The viruses are transported less far by the small droplets that you fire into the air by coughing, than by what you have on your skin afterwards.
Still, its better to cover your mouth with our ellbow when sneezing than to do nothing at all.
AND GO TO THE DOCTOR INSTEAD OF GOING TO WORK DAMNIT!
Definitely don't go to work but also don't go straight to your doctor - follow local advice which for here is to call the national health non-emergency line and take their advice.
We've had a couple of cases of local interest where people have just pitched up at Minor Injury Units declaring themselves to have Coronavirus and have caused lockdown and general hysteria.
I would suggest generally that if you're ill, stay home from most of your engagements, regardless of your recent travel, and get some advice.
I work in a mental health clinic setting, and in theory people shouldn't turn up physically unwell - but they do, they turn up having puked their guts up all night (when they have a bug, obviously its different if related to their MH). Most of the time, the odd cold isn't a concern - but now those symptoms should mean you consider staying home or at least getting advice from wherever your going and giving them the option of asking you to stay home. Just in our small setting, you could easily be sat in the waiting area for over 15mins with 10-15 people, plus an hour in the room with a therapist, and the therapist and the room are going to see numerous other people that day.
The risk will be similar in a GP setting.
The risk in terms of fatality isn't that high but people in general can be more careful about where they take themselves when they're unwell and think about limiting their role in the spread.