You may have "settled in" to a way of life by getting married, having a child, and having a job. This makes you middle class, at least, and perhaps Republican to boot! (Har har)
Your friends who call you square may be single, or childless. They may be liberal in their thinking. They may think their way-of-life is "cool" compared to yours.
Do you have a generally conservative outlook on life: political, religious, social? Do your statements give you away abut topics like alcohol? drugs? smoking? Sex? Do you speak for McCain and against Clinton or Obama during lunch or coffee breaks? Do you say anything about the current war in Iraq and Afghanistan that sounds conservative to their "coolness"?
I can barely remember when I was 23. My own kids (in their early 40s) probably can't remember when they were 23! They are all square. When I was 23 I took part in civil rights activities and demonstrations against the Viet Nam war. Is this the sort of thing you would see yourself doing? If not...square!
Why do you feel old, at 23? Maybe you're tired...being married and have a child and working can all tire you out. And if your friends are 40s-50s, that gives you the perspective of people older than you are, with what goes with people of that age: bodies breaking down, mid-life crises, problems specific to people their age but not yours, etc.
I would also ask: Since 23 is a fact, yet you "feel" old, what do you get out of feeling older than you are? (All human behavior is aimed at results or pay-offs in the future. What is the result you expect by thinking of yourself as older than you are?
I'm 70, but still feel like I'm 17 inside. You may want to try developing a different attitude (thinking yourself into a different way of seeing yourself) and getting some friends your own age who have viewpoints and enthusiasms of people your age.