Yes—your description gives some helpful clues, and you explained them clearly! The spider might be a green lynx spider. Green lynx spiders live in the southeastern United States, including South Carolina, and may hunt on flowers and other plants.
They are often green, with long legs that have noticeable dark, bristle-like spines. They do not build a web to catch their meals; they actively hunt insects. Those features sound like some of the things you noticed.
What we cannot tell for sure
Color and size can vary, and other spiders can also live on goldenrod. A spider looking flat from the front is not enough by itself to identify it. So this is a good possibility, not a certain identification.
What to do next
- Watch it without touching or trapping it.
- If you can, ask an adult to take a clear photo from a safe distance. You can show the photo to a local nature center, museum, or spider-identification group.
- If you cannot add a photo here, that is okay—your written description is still useful.
Spiders are important because they eat insects. Let it stay on the goldenrod, and enjoy observing it safely.