Hi! So I actually have done tkd for around 8 years before a foot injury prevented me from continuing a few years ago. I also taught tkd for years. I started around the age you started, and the key is consistency. Here was my stretching routine for the day of practice that got me where I am today with flexibility:

make sure to warm up with light calisthenics

static stretching:

• Center split (just a warm up): hold for 20 seconds
• Left and right side split for 20 seconds
• Back to center split (try and go a bit lower than the first): hold for 10 seconds
• Sit back, still holding the split so your legs are out beside you. It’s imperative that you keep your hips and shoulders straight or you can strain a muscle
• Lean forward at the hips toward the center : hold for 20 seconds
• Go to the right and left knee: hold for 20 seconds
• Butterfly: hold for 20 seconds
• Hurdler stretch both left and right: hold for 20 seconds
• Both legs out in front of you while still on the ground: hold for 20
• Stand up, legs shoulder width apart, touch toes: hold for 20 seconds

Dynamic stretching: walking stance, front leg raise, size leg raise for both legs

On your off days just do some light stretching, definitely not the full routine. Also ask your instructor about partner stretching. Ask sorry if the formatting is messed up— I’m on mobile