hi..thanks for your query.
From what you mention, it definitely does not look like psoriasis
.It is possible that the elbows might be coming in contact with something which produces a contact allergy
.You can have oral anti histaminics for sometime and apply a topical corticosteriod for a week.
If they still persist or the recurrences are very frequent , you should consult a dermatologist
to find a definite cure.
Hope this helps.Take care!