I live in Taiwan (English is my native language), and have studied Chinese to be passably fluent. I can trick people into thinking I can follow advanced conversations, interjecting comments here or there (even though I’m mostly lost – just picking out the tidbits I do understand and commenting on them).
But am I bilingual? At the end of the day, it doesn’t really matter. What matters the most is whether your level is “good enough” to do what you want! In my case, I just want to be able to go to the store, buy things, and hang out with friends. I can read the newspaper, but I’ll never be able to read/write business contracts – but that’s not a goal of mine.
There are so many different shades of bilingual. Don’t worry about it… and just be as good as you need to reach your goals!
I don’t cry when I chop onions. If I’m chopping dozens of them, everyone needs to get out of the kitchen because the air will get potent (but I won’t notice).