Hello in Jo-Burg,
TCA peels are a very effective way to improve skine tone, fine wrinkles and discolorations. They are not as effective with blood vessels below the skin for the simple fact they do not penetrate deep enough to do so (nor should they!).
TCA 20-30% combined with Jessner's solution is very effective and based on the degree of wrinkling you have very well may eleminate them. Prepping with Retin-A before and after the peel really enhances the results. The peel takes a week for all the skin to peel off and you will need to be very careful with sun exposure as you heal (sounds like you are already doing that).
Based on your description of the blood vessels, I would advise exploring lasers further with an expert who does facial lasering as one their primary areas of expertise.
It is possible that with the toning effects of the peel on your skin the blood vessels will become less visible - hard to predict without actually seeing you.
Other potential considerations are intradermal Botox or fillers to enhance the eye area and minimize the appearance of the blood vessels.
Hope this helps, Dr. J