The files in the syntax directory should be named after the filetype detected by Vim. In the case of your C++ code, I'd expect it would detect it as cpp. You can check that with the following command:
Or you can use :set ft? for short.
Once you confirm that the filetype is indeed cpp, you can create file ~/.vim/after/syntax/cpp.vim (for ...
Most probably you have set spell enabled which usually checks spelling in comments.
If you don't need it turn it off with :set nospell. Activate when you need it with :set spell.
To toggle use :set spell!.
Map it if you do it often, for example:
nnoremap yos :set spell!<CR>
Then yos will toggle spelling.