My obsession with processing things has made me a weaker person.

Because I used to keep all my feelings inside, and I failed to be angry enough when things were actually bad, I tend to be obsessed with the idea that I need to process something before I move on and stop angsting, and until then, I'd just act like the world just ended. It's like I no longer have much of a sense of soldiering on as I did before. I believe that I could learn from my younger self in that I should learn to have a sense of just keeping on doing things even when you secretly feel like it's the end of the world, and my younger self could learn from me how not to be OK with things when you shouldn't be.

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Meditation is perfect for this as it deals directly with the idea that thoughts are transient and abstract rather than huge problems that need resolving.

Perhaps look specifically at Vipassana meditation, and also mindfulness.