This is unlikely to be cancer.
The irritation apparently stimulated a precess such as eczema.
Eczema typically can be dry and scaly and appear in only one location, although there are several forms of eczema.
Squamous cell cancer can appear as red, scaly lesions, more often on the face.
To put your mind at rest, a dermatologist can not only diagnose the lesion, but do what is called a punch biopsy for the lab if this is needed [even your gp can probably do this part].
Obviously this can not be diagnosed with high accuracy on the internet, but a process such as eczema or psoriasis is more likely than cancer. If it is a cancer, squamous cell does not spread that readily, and taking care of it now will be prudent.
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