There's no age limit for songwriting or singing. You're never too old and your never too young to do both. You already know that you love to sing so songwriting is usually a nature progression after that discovery.
I began singing at the age of 3 years old and I wrote my first song at 10 years old. If music is your passion then that is what you should pursue. The best songwriters in the world are excellent storytellers. They know how to write a lyric that captures your attention and they can say something that just about anyone can relate to. The best songs are the ones that are honest and real. Why does everyone love "love songs"? Because at some point in our lives, all human beings have had a crush on someone or been in love with someone, so they can feel when song lyrics are sincere and genuine because of their own experiences.
What is on your heart? What experiences have you had in your life? What stories would you like to share? Write about what you know. That is where I suggest you start your songwriting journey. Stay true to yourself and you'll be amazed at what you can achieve. If you have any other questions, feel free to schedule a lesson with me.
Best of luck!