It is perfectly normal to feel old at any age. This because we are always getting older and our lives change because of it.
I felt old when I was entering full time work, missing no-responsibility days of high school or university.
I feel old now when my friends are getting engaged and married.
I feel old when I went to a friends kids birthday party.
However life is a journey, as you get old there are new things to experience.
Sharing your life with your significant other.
Moving into a career where you take pride in your work, where you like your job.
Buying a house, having your home sweet home.
Having your first pet. I had pets growing up but it is different when its your pet and not the families.
Things I haven't experienced. I guarantee I will feel old but I am also looking forward to.
Starting a family.
Seeing your child's first step
All inclusive holidays
Getting married
Retirement
If your are missing the fun stuff in life. Go traveling. Seriously I have never been so immature and had so much fun when I was backpacking. A good resource for this is the book vagabonding.