Rich people seem to manage all right with their billions and don't feel burdened by them. That includes people who were born to it, such as the Duke of Westminster, but also people from less exalted backgrounds who have made their fortunes - Roman Abramovich springs to mind. I reckon I could handle £184 million, given the chance, though I wouldn't announce my win. The line about "not having to keep explaining" if you go public wouldn't work, as I only have a small family and very few friends! I would swear my family to secrecy and tell my friends I was moving abroad....We would have a good farewell party, though.
The first thing would be to secure my children's futures and put money in trust for my grandkids. Then the best private doctors available to sort out our health issues. A nice house, of course, and lots of travel, including regular trips to see our elder daughter in the USA. And then the joy of being able to give freely to the homeless charity our younger daughter runs, plus Children With Cancer, Water Aid, Medecins Sans Frontieres, the NSPCC, Save The Children and so many more...
However, as I never buy lottery tickets, I don't think that it will be happening.