At least once a year around half of people in Switzerland decide to go to work even though they're not well. In technical jargon this is called presenteeism. They're at work, but aren't really achieving anything useful. In many cases people go to work sick for fear of losing their job, having pending tasks pile up, or leaving their co-workers in the lurch.
You're not doing anyone a favour if you turn up for work with the flu – least of all yourself. It can prolong the process of getting better, and in the worst case the flu will weaken your system so much that you end up with bronchitis or pneumonia. You also expose your colleagues to the virus. For this reason doctors advise staying off work if you have the flu.
Flu symptoms are more extreme than a cold, and include fever. You can read more here.
Unlike flu, a cold is no reason to stay at home. Even so, make sure you don't infect your co-workers.
You can treat a cold with home remedies. Generally it helps to wrap up warm, eat plenty of fruit and vegetables, and drink a lot of water.