The cry of your heart is clear, and you have already turned to the right place: the words of Jesus. You referenced the kind of spiritual bondage that requires prayer, and you are correct. But let us be sure we understand what kind of prayer opens the door for the stronger man to enter and plunder the house of the strong man.
If there has never been a moment where you came to God on His terms, then the only prayer He is waiting to hear from you first is the honest confession, "God, be merciful to me, a sinner." Relationship is the foundation. Without it, prayer becomes an attempt to use God as an instrument to impose our own will. True prayer does not start with our demands; it starts with the heart of God. He makes His will known to us, and our praying becomes the act of opening the door to allow Him to do what He already desires to do. His will is your deliverance, but He will not force it on you.
The type of oppression you describe, the physical pushing, the emotional turmoil, the shame, cannot be driven out by human effort or repeated words. Light and darkness cannot coexist. My role is not simply to pray a prayer of deliverance, but to pray for the entrance of the power of Jesus Christ into your life. When He enters, the darkness has no choice but to flee.
Given the intensity of this battle, listen carefully to what Jesus said: "This kind can come out by nothing but prayer and fasting." Fasting is not a hunger strike to force God’s hand or to prove your desperation. It is a practical way of dealing with the inner warfare between the flesh and the spirit. As you deny the physical man, you learn to feed the spiritual man. When you combine a fast with heavy feeding on the Word of God and prayer, you are strengthened spiritually. The weakened flesh loses its loud voice, and your spirit becomes more sensitive and more authoritative in Christ.
Your struggle is not hidden from God. Like David, you are being oppressed by an enemy that pushes you around. Make his prayer your own: "Judge me, O God, and plead my cause. Oh, send out Your light and Your truth; let them lead me." Do not focus on the social embarrassment; the enemy uses shame to isolate you. Instead, in the privacy of your own room, shut the door and pray to your Father who sees in secret. He rewards that open, honest seeking. That is where the true battle is won, away from the eyes of man.
As you abide in Christ and let His words settle deep within your heart, you can ask with a confidence that aligns with His will. The joy of seeing God work in answer to prayer is coming. Do not look for a reputation of being a person of prayer; just be a person who prays. Let your fast and your prayer be a quiet, determined strengthening of the inner man until the stronger One has fully entered and the spoils of your peace and freedom are fully restored.