No. Plethora is a term that we pediatricians usually use to describe a newborn that looks "flushed" or swollen looking with redish facial appearance. Answeing strictly your question and in this particular condition, it shouldn't be painful or bothersome to the newborn. If you are using the word to describe something else, please let me know and i'll be glad to explore your concern further.
Not. Plethora is not painful. It's describing a very red, ruddy skin color, which may be associated with the dilatation of the superficial blood vessels (flushing) or excess of red blood cells (polycythemia). It should be differentiated though from the disease 'polycythemia vera', which might have symptoms of plethora, fatigues, headaches, dizziness, itchiness, bloating, difficulty of breathing, etc.