[Syncro]

You have your terms a little mixed up.

...the term 'cotton-picking' originated in the southern states of the USA, where it is usually pronounced cotton-pickin'. It began life in the late 1700s and differs from the 19th century Dixie term, 'cottonpicker', in that the latter was derogatory and racist, whereas 'cotton-picking' referred directly to the difficulty and harshness of gathering the crop.

From Here

[MrB]

Yeah, I read the link.
It simply means that you have rough hands from the difficulty of the task.