If you are getting paid to do work (including designing or writing) then you are self-employed. That's a great thing, but it does mean you need to pay income tax and self-employment tax. A child's income earned from working is never reported on a parents' tax return, only on a tax return in your own name. However, unless you are paying more than half your support costs (your share of food, rent or mortgage, clothing, and all your other expenses), you can still be your parent's dependent.
You will need to start keeping records of your income and any "ordinary and necessary" expenses that are part of the work you are performing. There are more details to having self-employment income that you can take time to learn, the main thing getting started is to keep your own accurate records of your income and expenses. You are required to report your income even if you don't get tax statements (like 1099s) from your customers and clients; at the same time, if you do get tax statements like a 1099-K from PayPal, Patreon, or someplace similar, the income on the 1099 is not necessarily the amount of your taxable income, and having records will help you complete your tax return so you pay the correct amount and not too much or too little.
