Caterpillars are notoriously difficult to ID even from live specimens -- key features include head capsule morphology (not clear in photos), number of fleshy prolegs (rear feet - not photographed), presence of hairs, and only sometimes patterning. As caterpillars grow, the patterning can change substantially.
Texas A&M have put out an ID guide to different pest caterpillars
here. Fortunately, your caterpillar doesn't key out on this list, meaning it's probably not a major agricultural pest.
My best guess is that it's a moth larva in the family Noctuidae. There are a few other families with heavily spined/hairy caterpillars (e.g. tent caterpillars), so take this tentative ID with a grain of salt! The family Noctuidae contains both harmless moths as well as major agricultural pests. The majority of species don't do major damage, and a few are serious problems (e.g. the gypsy moth). If you can take some photos of the head, and a good side-on view, I'd suggest posting to iNaturalist or BugGuide to get a second opinion -- heaps of great entomologists are on those websites who might be able to help ID your sunflower-eaters!