Do you have to self isolate if someone in your house ?

No, the common cold isn't caused by covid.
If you don't want to get it stay away from them. Don't share things like cups and utensils. 

Right now yes in case it is Coronavirus. Once they are tested negative then no. 

"The common Cold" is a generic term. It can be caused by a number of different types of viruses - which is 1 reason why it's impossible to cure. One of these viruses is a type of Coronavirus. Covid-19 is but one type of Coronavirus and it does not cause the common cold. To make an analogy; a Ford Explorer is a type of car. Not all cars are Fords and not all Fords are Explorers. Car = common cold. Ford = Coronavirus. Explorer = Covid-19.

actually the common cold is MUCH more infectious

If it’s not COVID then no