Exhaust

I was driving and after aprroximately 200-300metres a light in the dashboard has came up and stayed, I looked it up in the manual and it says it is a fault in the exhaust system. What should I do? Could a reason for this being because I washed the car yesterday and may have got the exhaust wet? It had its MOT 2 days ago and passed it fine, no problems

The exhaust seems to have a small ring of black powder at the tip.