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I don't think you'd be rude for asking. Maybe you can say something like "My birthday is coming up and instead of gifts or a party, I would like people to share their favorite memory, photo, or something else about me. It would really mean a lot to me to hear from you, and I will carry what you share with me for a long time. These are things I can think about whenever I need encouragement." I think that it doesn't sound desperate but explains a bit about why you'd like this to be done without going into extreme detail.

I'm also wondering if as an add-on you can write down some of the highlights of the year. You can look at these and remind yourself that even though there have been struggles, some cool things have happened too.