My 5 month old budgie had vomited at night and we had noticed after opening the cage in the morning. Now he is not having anything and sitting very quietly and some changes had seen in his nose colour
Vomiting in budgies can be a sign of many things such as an impacted crop or an issue with the digestive tract. It could also be due to improper feeding as nutrition for a budgie is very important as they need to eat more than just seed which is a common mistake new owners can make (see this article for more information on feeding). However, vomiting in addition to not eating makes it even more important to see a veterinarian to help find the underlying problem as soon as possible as they need to eat regularly. Ideally, you can find a veterinarian that specializes in birds or exotics. They will be able to give a proper exam and see if there is anything obvious which is wrong and they may want to run some additional lab tests.
It is also important to note, that sometimes budgies regurgitate which can be normal behavior. Here is an article that discusses the difference: http://www.animalhouseofchicago.com/locations/illinois/chicago-animal-house-of-chicago/articles/bird-vomiting-regurgitation