You ever fall backwards with your eyes closed into the trusted arms of family or friends? With certain people in your life, you just know they will come through for you. Faith in Jesus is the same thing!
I know your sins are heavy and you wonder if Jesus is willing to catch you with all that extra baggage. . .but He is! When He died in the most horrific way possible, feeling all our pain and sin, He paid the price in full.
Once you realized that He is the Savior, He Himself feels the moment you did, and you become saved. From here on is the sanctification PROCESS. It's true that faith unlocked the salvation that only Jesus provides at the MOMENT of faith.
From here as you develop a deeper relationship with God, you become a new creature. You will understand in time how this all works. I myself am a babe in Christ. I felt like you did once, and was given a dream where I saw myself as a baby being bottle fed. I knew what He was trying to tell me!
Good luck on your Christian journey, but rest assured you are saved ☺