Stop being afraid of coming across as needy!
When it came to dating, I was always afraid of coming across as needy. Of course, to a certain extent, we need to do the internal work but it's so important to remember that having needs is part of being human. It's okay to lean on a partner to help you work on your insecurities.
If you open up about an insecurity, I would see how they react to that. It's very telling of a person and can let you know whether this person is the right fit for you. Your partner should not be the solution to your insecurity (or to happiness) but a partner can recognize your insecurity when it does flare up and help soothe you when you need it (in addition to your own self-soothing!)
It's okay to share your insecurities. It's not needy to lean on a partner sometimes.