Advice please?

I've been dealing with depression for a couple of years now but for some reason I think my actions are slowly making it more and more obvious that I'm not okay especially to my parent's as my current situation requires me to be around them pretty much all day.

My parents don't know that I have depression or have been dealing with suicidal thoughts for years now because they honestly just don't believe in mental illnesses and I've never been that comfortable to discuss it with them in the first place. Whenever it's brought up (via news/gossip), they say things like how mentally ill people are scary and crazy, how they should be locked up and etc as they carry the typical traditional beliefs of asian parents. Obv as I heard this when I was around maybe 10 when I first started experiencing symptoms of depression and since then it has caused some communication problems as I genuinely have a hard time vocalizing to anyone and everyone because it's something that I just never got to do and today I felt sick and threw up because of a panic attack of sorts and I know exactly what caused it but my parents want me to bring this up at my next doctors appointment (on monday) and ask them why it's happening and that they'll be coming with me to it.

I don't know how to approach it at all because I know exactly what's wrong with me and why I'm experiencing stuff like that and for me to tell a doctor about it as my parents are in same room is a hard no for me. It's not something I can just suddenly get better on but also not something that my parents will just let it gloss over with so I'm really scared and don't know what exactly I'm supposed to do.