Hi! I want to start this by assuring you that you are really not alone right now. Everything you said in this post resonated with me greatly; as someone who has been bullied, has emotionally challenging parents and persistent (yet sometimes fluctuating) low mood.
Firstly, you are absolutely worthy of getting help. Something a lot of people don't realise about depression - especially high functioning depression (which this sounds awfully similar to, with the good academic performance and extracurriculars) - is that you don't need to be low all of the time to be depressed. Those moments where you're okay are extremely confusing, I know, because it's almost like you try to convince yourself the low times aren't THAT bad if you can still be okay. This isn't true. Your emotions and feelings and experiences deserve to be taken seriously.
If you want to tell your parents but are unsure how, then I am firm believer of writing things down. From this post alone, it seems like you're really good at this. Whether this is in a text or a letter, this could be an option. It doesn't have to be detailed. Even something simple, such as when you're in school/college/uni (idk how old you are) so you don't have to immediately deal with a potentially uncomfortable conversation.
I do believe that therapy is a good idea. If that's inaccessible, then speaking to a teacher, friend or your parents is definitely something you should do. I personally accessed counselling services outside of my college. They were able to refer me, my parents had no idea, and I was able to receive six weekly sessions this way. I think exploring your options through your school is a good option for this reason. If you're worried about accessing school counselling, then I would speak to a teacher about confidentiality first.
Most schools have a duty of care to report anything that means you're in harms way. If you express thoughts or experiences of this nature, they'd probably have to tell your parents. But, if you are safe, then speaking to somebody in school shouldn't be an issue in this regard.
The conversation of getting help is always the most difficult. But, trust me, you want to do it now. I let everything escalate and things became far worse. You DESERVE help. You have been through so much (I'm pretty sure bullying can be a form of trauma). And now this low mood is interfering with your daily life. I don't know your situation with friends, but if that's an option, reaching out to them would also be a good idea. You'd be surprised how many people struggle with everything you have described. Just having someone to empathise with you can sometimes mean the world.
If all of this sounds too daunting, I can reply to this with a non-anonymous post so you can message me about whatever is on your mind. You're not alone!!!