The name applies to several species:
Since your ancestors were in the Carolinas and used large buds, balsam poplar (Populus balsamifera) is almost certainly the plant. It grows in the Carolina mountains. Search for nurseries stocking this native poplar to confirm bud characteristics match your family's salve recipe.
Balm of Gilead
Bee Balm (Monarda didyma): Red Flowers for Pollinators and Tea
Bee Balm 'Jacob Cline' (Monarda didyma): Mildew-Resistant Red Cultivar
Lemon Mint (Monarda citriodora): Citrus-Scented Bee Balm
Bee Balm 'Raspberry Wine' (Monarda didyma): Deep Red Cultivar by D. Probst
Agastache 'Pink Pop' (Agastache austromontana 'Pink Pop'): Compact Hummingbird Mint
Basil Bee Balm (Monarda clinopodia): White-Flowered Monarda
Eastern Bee Balm (Monarda bradburiana): Early-Blooming Native for Dry Shade
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