You recognize your current problem and you're able to associate it with your past trauma. Victims of sexual abuse respond in many ways besides shutting down. The vast majority of sex addicts have experienced sexual abuse. You have your whole life ahead of you, and the fact that you are able and ready to face your traumatic past and your current unmanageability portends well for your future.
You may find a certified sex addiction therapist in your area through www.iitap.com, and there are also many great and helpful 'S' groups that are free -- these are 12-Step Fellowships that focus on Sex Addiction including SAA, SCA, and SLAA. A simple web search will bring up more information. Typically sex addicts find recovery through a combination of counseling for sex addiction and 12-Step recovery. There are also inpatient centers that specialize in sex addiction or offer outpatient intensives.
Take the HBI - Hypersexual Behavior Inventory test here and see how you score:
http://thecenterforhealthysex.com/tests/hbi_hypersexual_behavior_inventory/While sexual virility seems to be the stereotypical young man's dream, what you describe when you "can't seem to get enough" is the painful reality of the constant unfulfilled hunger resulting from addiction where the fix no longer fixes anything. Everyone becomes sexualized, which results in disconnection and lack of intimacy in every relationship. Just as a drug addict turns to drugs to self-medicate from life's pain and problems, a sex addict turns to sex to avoid feeling pain, stress, anxiety, grief, etc. This is a progressive disease meaning that it gets worse. Addicts typically risk their physical health, their legal health and their psychological health as the behavior escalates in search of a better 'high'.
Please seek out help, your life is worth it.