Yes, you would be subject to paying self-employment taxes. Being a minor has no affect on whether or not you owe self-employment taxes, unfortunately.
You would file your tax return on Schedule C. The information from that schedule flows to your individual income tax return (Form 1040).
If that is the only income you earned, your parent(s) (or other guardian) are likely claiming you as a dependent on their tax return. So, be sure that your tax return is marked appropriately indicating that. Also, if that is the only income, you will likely not have "taxable" income subject to "ordinary" income taxes, but the "self-employment" taxes would still be required to be paid. That is, unless you have some sort of credits to offset it. This is highly unlikely as a minor.
The following links may be helpful:
How do I report income from self-employment?
https://ttlc.intuit.com/replies/4801198
Why am I paying self-employment tax?
https://ttlc.intuit.com/replies/4799028
