I would define a pedophile by both their actions (any sexual contact with children) and also their distorted belief systems (children want sex, children are seductive and they cause their own sexual abuse, sexual abuse does not hurt children, touching and fondling is not harmful, if I am not violent I'm not hurting the child, if the child doesn't fight back it's not sexual abuse, and on and on and on.....).
As you can see, a pedophiles belief system is a collection of outlandish distortions and lies. These rationalizations, denial and lies serve to make the pedophile more comfortable with what he has done to innocent children.
It sounds like you know right from wrong. You know that any sexual contact with a child is wrong and you don't want that. It sounds like you are bothered by your physiological/sexual reaction to children. A pedophile may be bothered, but he does not seek guidance--he just further denies his feelings. If he acts on those feelings, he further distorts reality to support the sick stuff he does. You sound very conscientious. You do not sound like a pedophile to me. I applaud you for asking these difficult questions.
I'm a survivor of sexual abuse. I have learned a great deal about the horrible effects of sexual abuse--which can last well into adulthood. One thing I experienced, while changing my daughter's diapers--is the notion that children are sexual. This bothered me horrendously. My therapist said that most survivors experience this. Survivors will have sexual feelings for children or they will see children as sexual or sexy. These feelings are disturbing to the survivor. My therapist said that when children are molested, the notion that "children are sexual" is carved into their psyches at a very tender age. When chidren are forced, by predators, to be sexual objects, this may lead to a child correlating children with sex.
First let me say that I am not a therapist, nor am I qualified to judge your past. However, your post struck some chords with me, and I am wondering if you were ever sexually abused. Do you have any memories of anyone sexually abusing you? Did you ever act out sexually as a child? Acting out as a child is a huge red flag that sexual abuse has occurred. I know that when my children hit the age of 2, these sexual thoughts started---and other relatives have confirmed that my abuse began at around 2 and a half. My daughter's naked bodies triggered the memories of my own 2-year old body and the sexual abuse it had endured. I learned to understand that I was not desiring to sexually abuse my children--I was simply remembering feelings about what happened to me. I learned to understand those feelings and they have since disappeared. It sounds like your body may be automatically reacting (and possibly remembering) sexual abuse, much in the same way that I was remembering my own abuse.
I applaud you for asking these questions--and I also want to caution you. These feelings are NOT normal. These feelings are a sign that something is amiss. Most pedophiles begin with these feelings only, too. Environmental triggers, their own dysfunction, selfishness and other factors--cause them to act on their behaviors. I would not leave this unchecked--for one nanosecond--especially with children in the house. My father was not a pedophile, until our family broke down and financial troubles triggered stress. My father must have had the distorted thinking--but he didn't act on that thinking until extreme environmental stress triggers caused him to completely go off the deep end. It's a gamble to not take care of this.
If you were abused at a very early age--you wouldn't remember it consciously, but your unconscious mind would have made the connection between sex and children. If that is what happened--then it is essential to find a therapist who can help you work through your past. You don't need to remember abuse details to heal from abuse. Often, abuse is evident by our symptoms. Getting erections around children may be a red flag that somehow, someone was sexual with you.
Only a qualified therapist can judge your situation accurately. I would find a good therapist who specializes in sexual abuse.
Also, most pedophiles are married men. Our society has a distorted view of who the pedophile is. I think most pedophiles don't believe they are pedophiles--because of society's sterotype of the scraggly, toothless old man hanging out in parks in a dirty trenchcoat. My father is a respected business owner who lives in a upper-middle class neighborhood. Most of the survivors in my support group come from intact, 2-parent families and their fathers are insurance salesmen, doctors, pastors, accountants, police officers, carpenters, etc. My therapists treats pedophiles and he describes these guys are "average joes" with above-average intelligence and most are good looking. This is one reason why survivors don't come forward. Society does not want to accept that the financial consultant next door is molesting his children. Society is in denial. Everyone wants to feel safe, believing that pedophiles are dirty and easily detectable. Most molestations occur in the child's home, by someone in the immediate family or someone the family knows very well. It is not a rare occurence either. Most studies suggest 1 in 4 females and 1 in 7 boys is molested before age 18.
I think you are brave for posting here and I hope that you find a qualified, experienced therapist who can help you sort this out. I wish you the best of luck and I commend you for being conscientious enough to come here and ask these difficult questions. If my father had one tenth of your courage, thoughtfulness and compassion--I would not have suffered through years of therapy for PTSD, eating disorders, panic attacks, depression and other symptoms of profound trauma.
You are a good man. Now, go find a good therapist.