First off, hi there everyone!
To give a little background on myself...
My family never was very religious, however, my mom would take me to church every once and a while when I was younger and I was baptized at age 7. I would say that I always believed in God and Jesus, but I never really thought about Christianity seriously until the past year or so (you know what I mean?) so I consider myself a new Christian. Anywho, I was wondering if it would be ok if I got baptized again. It's something I would love to do because now I'm actually a believer and my previous baptism was kind of a "whatever" type thing (if that makes sense).
Baptism is not something that saves you. You're not going to lose salvation by mistreating baptism. But baptism is instituted by your Savior. The issue will grow to bother you later on, if you don't pass through this time with some things settled about your prior baptism. It's likely time to sit down and hash through this with your spiritual leaders -- preferably those who don't, by foregone conclusion, baptize everyone regardless of how often they've been baptized.
Baptism isn't a sign that you've become a super-disciple. It's a sign of your faith. I think the real question is whether you thought your family had faith in the first place. Excepting Christmas/Easter Christians, it's quite a bit of effort taking a kid to church. There may have been more behind all that than it first seemed.
How you felt about the baptism also doesn't factor into it. Like signing a contract, you may not have known entirely what you were getting yourself into. But that's become clear now more than ever.
You said you believed in God and Jesus -- but your maturity in coming to Christ of your own accord now, that's a sign that God has been working in you all this time to bring you greater awareness of His love and grace. That warrants a public profession of faith and a public testimony to God's work in you.
Baptism is a one-time thing according to Scripture (Ep 4). You're essentially either denying the validity of the prior baptism, or you're asserting the superfluousness of baptism in general.
Simon the Sorcerer was not rebaptized. The adulterous man in 1 Corinthians 5 was not rebaptized. The Apostles were not rebaptized (in water) after receiving the Holy Spirit at Pentecost.
Finally, the idea that children aren't baptized is ... inconsistent with Scripture. Ephesians 6 holds instructions to children
in the church. Every other group of people Paul is talking to, are people
in the church. It would be odd to think these children weren't part of the church. And being part of the church in the First Century involved being baptized (Acts 2:38-40).