If you take baths that's a great time to try pulling it back, when it's been soaking in the water for a while. It may feel funny pulling it back but you can stop if it begins to hurt. Then try again the next time you're in the bath. Just keep trying and stop when/if it hurts. Don't even think about getting circumcised. That removes over half of your pleasure producing nerves and it's not fair to your future wife either.
I never had a problem because my mother always pulled mine back to wash under it until I was about 5 then she made me do it myself. So I was always able to pull mine back. By the time I was your age I was pulling it back a lot because it was fun to play with.
You can Google frenulum for plenty of pictures.
That's a great picture you found in Wiki. If you look you can see he has the foreskin pulled all the way back off the head. That's how it's supposed to work and most guys have no problem doing that. So don't get your mind all screwed up listening to the possible problems because most guys don't have those problems.
Your glans is sensitive but it's not bad to touch it, it doesn't damage it. It's sensitive partly because it's been covered all it's life and partly just because that's just the way it is. Right now you don't need to worry about that. The first thing is to get that foreskin back so your glans gets to meet the world.
Your penis is not going to fall off or any other bad thing if you don't pull it back to wash it, and you don't HAVE to be able to pull it back to have sex. Nothing bad is going to happen to you if you can't pull it back. I don't know why your mother would tell you such a thing. She should be helping you with this. That's what mothers are for.
Getting it back so you can wash it is just a lot nicer for you and your lover and sex is a lot more enjoyable with a foreskin that rolls back and forth easily. So is masturbation. It adds a great deal to your pleasure if you can pull it back and stretch it back a little bit. The inner side of your foreskin is designed to give you a pleasurable feeling when you stretch it back.
So just pull it back, stop if it hurts. If that happens we can discuss that then.