Is PRP safe around the eye?

PRP under the eye can be very safe and effective for thickening the collagen layer and reducing the appearance of dark circles. The safest way to apply it to this area is to use a dermal pen. Injecting under the eye is more effective but has some risk because PRP is full of platelets that mediate clotting, so if it is injected directly into a vessel then it can occlude a vessel that goes to or from the eye. I do this injection frequently and in some patients with pronounced veins in this area, I may use a high resolution ultrasound or other docs may use a vein finder (green light that makes veins visible on the surface) to avoid any vasculature. In most cases, I avoid this complication by drawing down on the skin below the eye, injecting just beneat the surface at a few different sites and massaging it throughout the entire area. This is where the skill in application makes the biggest difference in achieving the best effect, safely. 
Lastly, not all PRP is the same. In order to get an adequate concentration to have a meaningful effect you need to draw 10 x the amount of blood as you want PRP, ie 60cc to get 6 cc, which is enough to cover an entire face. Under the eye may take 1cc total between using a dermal pen and injections. Most aesthetic practices use inexpensive kits that draw about 10 cc of blood to obtain 6cc of PRP, which is only concentrated by 1.5-2 x baseline platelet levels (inadequate for any type of regeneration). There only a few kits that actually concentrate platelets by the necessary amount ( 600,000 -1.5 million platelets/ml where the baseline can vary from 100-250,000 platelets/ml, ie at least 5x concentration is necessary in most cases). Some kits that adequately concentrate PRP also contain too many Red Blood Cells, which contain iron, that is both inflammatory for the skin and can stain the skin, ie one of the main causes of dark under eye circles is “hemosiderin staining” or iron deposition from red blood cells under the skin. 
With a dermal pen there is minimal to no risk of getting a black eye or bruising but you will look red and raw. With an injection you will be puffy under the eyes for 2-3 days or sometimes up to a week but it will get progressively better. It is also possible to have bruising or a pretty good black eye for up to a week with an injection. If this happens then I use BBL (Broadband Light Therapy) to break down bruising along with Skintyte (infrared wavelength) which helps lymphatic drainage. This can decrease the time of a visible bruise from a week to a day or two. It is best not to ice so as to allow the lymphatic drainage to evenly distribute the PRP. Elevate your head over the next 48 hours (sleep with a few pillows) and avoid anything that increases blood flow (ie exercise), which may increase the size of the bruising or swelling. 

Platelet rich plasma is slowly advancing into a vast treatment with multiple uses ranging from the hair, face and breasts with more to be explored. In recent times, it has been trending as a treatment for dark circles under the eyes.
Is it safe?
Under the hands of an experienced surgeon and the right delivery method, yes, platelet rich plasma under the eyes can be safe.
Does it truly work for dark circles?
Dark circles can be caused due to many reasons (like volume loss, pigment deposit, thinning of the skin etcetera). Therefore, there is no one-size-fits-all treatment, the treatment needs to be personalized to each patients root cause of the problem which can be a combination of one or more causes.
So PRP may help with the fine lines or wrinkles like crow's feet that surround the eyes, however, it alone is not sufficient. It would need to be combined with other treatments like fillers, botox etcetera.
What are the potential side effects?
Though platelet rich plasma is wonderful in reducing fine lines and wrinkles, it can pose a danger to sensitive regions like the eyes. There have been cases where patients have faced blindness because of a thrombus/thrombi (blood clot) caused when the platelets where injected too far into the larger blood vessels.

Thank you for your message! PRP is absolutely safe to use under the eyes! We often use a combination of treatments for the under-eye area, and a consultation with a provider in your area would likely benefit you best! We usually use a combination of modalities with the PRP, including microneedling the area and straight injections to the area. Usually multiple treatments are required, though over time the area will improve in skin texture, the hollows likely will improve, and the crepey quality to skin will improve, as PRP helps to boost collagen.