Hi! Good to have you join the Dev Community.
ChatGPT and the API are in fact two separate product offerings. The ChatGPT Plus subscription does not provide you with access to the API.
In order to get started with the API, navigate to the developer platform on platform.openai. Under settings, select billing and then add a payment method. The billing system was recently changed to pre-paid, meaning that after you have added your payment details you need to add credits to your account first in order to access the API. Once you have added the credits, it may take up to 30min for them to be available. For reference, please note that the documentation still indicates that there is a free tier. OpenAI has however recently discontinued the initial free credits. Hence, unless you add credits you will always face the above error 429.
For a technical overview on the use of the API, you should take a look at the developer quick start guide along with the more detailed other documentation.
I hope this helps to get you started.
Good luck with your project.