VI Precision Peel treatment - wish it gave me more renowned results

I had my VI Precision peel treatment at $275. My skin is pretty good than earlier but i see i got many small whiteheads under chin and around nose. Also, i did not at all peel undereye. My asthecian told she did apply chemical peel solution under my eye till eyes lashes but i see that area still very dull n rough. I wish little more was applied in that area in order to peel my under-eye skin. Moreover, my acne marks/ blemish are still there i do not see much difference in dark spots they are still dark. I think that peel was moreover superficial peel not medium -to deep. I wish it gave me more renowned results after spending $270 but now i m thinking on thought of getting or not getting second session of VI chemical peel