I've actually faced this issue, not just in my romantic relationship but also in my family relationships and with my friends. I used to have severe depression and self-harmed a lot. My therapist told me that I had become what's called the IP- the Identified Patient. When I was depressed people felt like they had to crowd in and support me or rescue me from myself. This took a toll on them and eventually it can cause conflict in those relationships when the other person has difficulty always being in the caretaker roll.

Honestly what helped me was owning my emotions. I realized that I had difficulty facing my emotions and that I was taking them to other people to "fix" them or to give me reassurance or to make me less depressed. Some reassurance is fine, but it's important to be able to process your own emotions, find ways to cope, and give/show yourself reassurance and compassion. These can be hard skills to learn but they are possible. Working with a therapist on these skills can be incredibly beneficial, and therapy is often helpful for people with mental health issues. A therapist would also be a third party who could help you talk about things with someone other than your boyfriend.

It's okay to be open with your emotions. Being open with your emotions is very important. However, there's a difference between being open with your emotions and asking others to solve your problems or make you feel better. Let me be clear, I am not saying this is what you do, but this is something I have often observed in myself and in others, so it's pretty common. It's okay to ask for help, but I would begin to differentiate the times when you REALLY need help and when you can handle it yourself. Maybe you could start by handling small crises on your own. Instead of automatically going to your boyfriend, you could instead try to use therapy skills to handle your depression before turning to others.

You could also phrase the way you say things differently. Instead of saying "I'm depressed, help me," you could say "I want you to know I'm feeling depressed right now and I'm trying to handle it on my own, but right now I'm really struggling. Could you maybe suggest a skill I can use to be more effective at managing this?" That way you do ask for help, but you ask for them to help you help yourself. It shows responsibility for your emotions.