DALL-E 3 isn't available via API or labs. If you don't use ChatGPT you get the (significantly lower quality) DALL-E 2 at the moment. That's supposed to change by the end of fall.

One of the most frustrating things with "Open"AI is you can't just use what they announce as available, you have to wait for an A/B rollout (as a paying customer!) or for it to be accessible in direct way instead of going through multiple models when you just want an image.