Is it necessary to wear clothes that must have black colour in them till the chehlum or 8 rabiulAwal or we can wear other colours as we are in professional life so we have to go on work places?

No it is not must. Black cloth is symbol of mourning and Ahlul bait as they wore it.
You May do one thing wear black cloth in majalis and at place of work other colors but avoid red yellow and orange colors
These are symbol of happiness and joy.