Why isn't there vaccine for the common cold?
Could we make a vaccine for coughs and colds?
Not easily because (a) there are hundreds of different types of cold virus and (b) they're continuously on the move. They're a moving target because they use a genetic form of information called RNA which makes mistakes when it copies itself and that means that they're continuously changing their shape. It's like having a facelift at the level of a virus on a daily basis so you don't recognise them from the perspective of your immune system very easily. They can easily re-infect you and a really good example of this is norovirus which is causing diarrhoea and has had 3 million people locked to a loo seat for longer than they'd like in the UK this year.
Norovirus is an example of this. It very quickly adapts and changes its appearance so, even though you've had it once, six months later you can catch it again because it looks entirely different by then.