Elsa, I overthink as well and for me is all day and everyday, that combined with anxiety disorder and chronic deppresion really takes me down, I've been fighting against this for almost all my life, I try to keep my mind busy to avoid going to dark places because of overthinking.
What has helped me is trying to slow down, listen to soft music (I love piano music, but I also listen to some soundtracks that I like), taking a walk, going out of the city everyonce in a while, I have my support group (family and close friends who are available to me in case of a severe crisis) and having my periodic checkups with a professional, I had to start taking meds because I was getting worse, the first thing the doctors gave me was something to slow down my mind at night so I could sleep, that along other meds to treat deppression and anxiety is what keeps me going.
What I've learned all these years is that you may have a lot of methods or ways to calm you, but if you don't really get help, then what you are doing is just surviving and sooner or later you are going to get tired of fighting and develop higher levels of anxiety and maybe depression.
Stress is one of the worst things to have when you suffer from overthinking and overthinking gets you stressed, is a vice cycle, but you must find the ways that works for you to relax, the more relax you are the less you overthink, also if you suffer from anxiety and/or depression, get proffessional help, it's the best way, they may give you meds or not, everyone is different, but the help you may receive will make you feel safe, well, only if you feel comfortable with your doctors, if not it will not help at all... been there... look for the treatment that works for you, take what you feel comfortable with and make your own method, one that works for you and you will feel better, it may take time I won't lie, but it will get better.
About trying to avoid relying on other people... DON'T... no matter how strong you may be, sooner or later you will get tired, you need to relieve the pressure that builds in your mind (your feelings, fears, thoughts, etc.), and the people who get annoyed because of how you overthink, I think everyone that suffers from this can relate, it has happened to us, you just need to learn to dose the way you relieve the pressure, I don't know how to explain it, its something that happened to me a few years ago, I learned how to relieve the pressure of my mind in a way that my friends and family don't feel annoyed and get the relief that I needed, now, they get annoyed when I have a severe crisis because I don't talk to them before it gets bad, the problem is that I get really bad late at night and I won't wake them up unless is a real emergency and my meds aren't enough.
And for the record, I'm 34 and was diagnosed like 14 years ago, before that, I was fighting agains my own mind alone without knowing what I had, I've been with anxiety dissorder since I was like 2 or 3 and with depression since I was 8.