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A plus sign after a Latin name indicates that the species is further divided into varieties or subspecies. 
Your search found 32 taxa.
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Common Name:
Eastern Swamp Milkweed
Corolla lobes reflexed; corona horns longer than corona hoods & incurved, per Vascular Flora of the Carolinas.
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Common Name:
Smoothseed Milkweed, Swampforest Milkweed, Swamp Milkweed
Stems conspicuously leafy. Flowers hoods have prominent protruding horns, per Atlantic Coastal Plain Wildflowers.
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Common Name:
Whorled Milkweed, Narrowleaf Milkweed
The petals turned downward, the upright hoods topped by protruding horns, per Atlantic Coastal Plain Wildflowers.
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Common Name:
Butterfly Milkweed, Common Butterflyweed, Pleurisy Root, Wind Root
Pollinator at work... Corolla lobes reflexed; corona horns shorter than hoods, per Vascular Flora of the Carolinas.
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Common Name:
Purple Savanna Milkweed, Red Milkweed, Bog Milkweed
Strongly reflexed purplish-red/lavender corolla lobes & orange-tinged hoods, per Atlantic Coastal Plain Wildflowers.
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Common Name:
Few-flower Milkweed, Red Milkweed
Corolla lobes reflexed, spreading; corona horns shorter than corona hoods, per Vascular Flora of the Carolinas.
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Common Name:
Poke Milkweed, Tall Milkweed
Corolla lobes reflexed; corona horns arching high, 1.5-2x long as corona hoods, per Vascular Flora of the Carolinas.
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Common Name:
Clasping Milkweed, Blunt-leaved Milkweed, Wavyleaf Milkweed
Corolla lobes reflexed; corona horns 1.5x long as hoods, arching [inward], per Vascular Flora of the Carolinas.
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Common Name:
Four-leaved Milkweed
Corolla lobes reflexed; corona spreading, its horns shorter than its hoods, per Vascular Flora of the Carolinas.
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Common Name:
Common Milkweed
Corolla lobes reflexed; corona horns more or less equaling the hoods, per Vascular Flora of the Carolinas.
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Common Name:
Fleshy Milkweed, Pinewoods Milkweed
The hoods are whitish, the petals ashy to pinkish-gray & strongly reflexed, per Atlantic Coastal Plain Wildflowers.
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Common Name:
White Milkweed , Red-ring Milkweed
The petals are flaring, the hoods sac-like, and the horns very short, per Wildflowers of the Southern Mountains.
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Common Name:
Purple Milkweed
Petals down-curved, hoods erect, horns sharply pointed & shorter than hoods, per Field Guide to the Rare Plants of Georgia.
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Common Name:
Michaux's Milkweed
Blossoms have very visible horns, whereas those of A. longifolia lack horns. — Will Stuart
Common Name:
Pineland Milkweed, Green Milkweed
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Common Name:
Longleaf Milkweed, Savanna Milkweed
Corolla lobes have rose tips; corona horns absent, per Vascular Flora of the Carolinas.
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Common Name:
Green Milkweed
Corolla lobes strongly reflexed; hoods long, narrow & erect; horns absent, per Wildflowers of Tennessee, the Ohio Valley, and the Southern Appalachians.
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Common Name:
Stalked Milkweed, Savanna Milkweed
Flowers erect, borne in 2-8 flowered umbels at the tip of a 1/4-1/2" stalk, per Atlantic Coastal Plain Wildflowers.
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Common Name:
Green Antelope-horn, Spider Milkweed, Green Milkweed
The petals are green and spreading (not reflexed); the hood is purple, per All About South Carolina Wildflowers.
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Common Name:
Bluevine, Sandvine, Honeyvine