feel bad 不是 don't feel well 的同义词
don't feel well = 身体不舒服
而 feel bad 通常用来形容做错了事的感觉 (feel bad about sth.)
和 don't feel well
有相同意思的习惯习惯说法是
feel rotten
feel miserable
I didn't feel well yesterday = I felt rotten yesterday = I felt miserable yesterday
我是加拿大人,前英语老师