This can be normal, but that doesn't change that once you got into the thoughts of hurting yourself, you should seek guidance, as you are now, so good job with that. But if possible, speak to your parents, its their job to help guide you through times like this. Don't assume they don't have time until they actually say or react to your issue by not giving you time.
Being a teen is frustrating due to the growing pains of exiting being a child and entering the years of those expecting so much more of you when you don't even know what to expect of yourself. You don't know what you want out of life outside of what your taught, and you often get lost in the reflection of yourself through the perspective of others. No one understands you no matter how much they know exactly what you're going through. You aren't as cute anymore. Welcome to the teenage years.
It doesn't have to stay this way. Sit down, or go for a walk. Think about how you often spend your time when you aren't in school or doing chores. Sometimes all you need is some healthy extra-curricular activities to keep you from sinking within your own thoughts as your mind grows from all the new things you're learning as a young person. Look into keeping yourself occupied with something that challenges you but you can also find joy in. Sports, school clubs, a part-time job, or volunteer work, or perhaps learn an instrument or take up art. Whatever you do, don't buy into your thoughts of depression. You aren't broken, you aren't a lost cause, you just need to reach out to something or someone, whether it be the activities i mentioned before, your parents, another family member, or as you said, maybe even a doctor. Just don't let them answer your concerns with a prescription. Drugs are an absolute last resort.