What to do?

You should always do what makes you happy. You said you don’t feel confident wearing your hijab. Is this something worth exploring? What’s your personal connection to your religion?
You should never let your family stop you from doing anything you love. If they love you, they should support your decision to be with your boyfriend. Talk it through with them and see how they react; it may be better than you think.
Moving to Korea would be a big and complex, expensive decision, so you should also make sure this is something you 100% want to do and can afford before deciding. You should plan it very well, and tell your parents when they are in a position to listen openly to your decision. Own your decision and don’t let them arrange a marriage you are going to be unhappy in.
You only get one life, so own it and do exactly what YOU want to do.

If you aren't already you should definitely try to get therapy for your depression – the NHS have started online CBT so you don't have the long wait. Know you aren't alone and you always have people to talk to, even if it's randos on TSR lol.
I can't really give you appropriate advice given I'm not a Muslim and wasn't brought up in your culture so my knowledge on any kind of rules in Islam is shaky at best, but general life advice would be to do what makes you happiest since if this turns out to be the only chance we get to live on Earth, it would be pretty crap if you didn't live your best life and you never get any kind of do-over. God/Allah must've given us life and free-will so that it can be used I guess? If you're going to regret not following the path you think is right for you for the rest of your life, then why follow the other path?
So long as you are safe and financially independent, you'll be able to think for yourself and make the decision based on what you think will be right.

Thank you soo much for the advice.
Since I have been restricted from doing things e.g. going out with friends, dying hair, getting nails done, travelling abroad I feel quite distant from my religion. My parents are very strict so I never had a social life. I do believe in God though.
What if they never accept me moving to Korea? What do I do then?

If they don’t accept you moving to Korea, then you should do it anyway. When you are an adult, they have no legal right to stop you. Live your life for you! I really hope everything works out well for you. If you do move to Korea, I am sure you will have an amazing time. It’s something I would love to do myself one day :-)

Thank you
Do I need my parents permission to do this therapy? I would rather have them not know.