You can send it, but you can't send it in bulk. You should send it by small parcel. Because I once met a patient who said he would take a bunch of Chinese medicine on a plane. When he passed the security check, the bulk Chinese medicine was not allowed to pass the security check, but the small package could pass. So I think you should be the same. Bulk is not good, small packaging should be fine.
I don't think there should be any special procedures, it should be the same as others.
If you don't mail it, you can ask a friend to take it with you if you go to America.