I have pockets of fluid under my eyes after Botox. How long will this last?

If the accumulation of fluid under your eyes is a product of Botox it should only last 3-4 months. In the mean time you can sleep with your head slightly elevated to decrease the collection of water. If you are still experiencing this after 3-4 months schedule an appointment with your injector to discuss options going forward. All the Best. 

The bags that you notice under your eyes may be a result of
pseudoherniation of the infraorbital fat pads.
Botox injections low along the crow’s feet can diffuse to the
orbicularis oculi muscle in the lower eyelids.
When this muscle is affected, the lower eyelids, which act as a sling
for the orbital fat, become relaxed. The
relaxation of support may lead to temporary pseudoherniation of the orbital
fat. This problem usually resolves as
the orbicularis oculi muscle regains function.
It is important that you see a board-certified facial plastic surgeon to
discuss these problems and to reduce your risk of complications in the future.

Your doctor is probably right, that the botox has weakened the muscle around the eyes and it is not able to effectively pump out the fluid and has created these water bags, or festoons.  While the usually resolve, there are things that can help expedite recovery such as lymphatic massage,  icing, sleeping with your head elevated, taking Benedryl to dry you out at night, in severe cases a water pill may help.  It is unusual for it to last this long however and make sure it's not related to having had filler around the eyes in the past (which can exacerbate this), having had eyelid surgery in the past (another risk factor for festoons after botox) etc.   I am finding that ThermiRf smooth is helpful with festoons in general and may help in tightening the skin of the lower lids in general to help prevent this re-occuring in the future.  If your doctor is not responsive to you and the condition persists, see an oculoplastic surgeon and injection specialist because there may be an underlying cause as well which perhaps can be addressed.Best of luck!

This is very unusual. I have never seen persisting swelling after Botox. To comment I would like to see before and after treatment photos.

I would be interested to see a close up picture of this.  I am wondering if it is truly fluid or just lax, loose skin forming a bag that resembles fluid swelling.  Sometimes when Botox is placed in the under eye for crow's feet and banana roll muscle treatment, and your skin is already lax, the under eye can end up looking worse with bags.  If it is lax, baggy skin worsened by Botox then I would recommend radiofrequency skin tightening if your darker skin or fractionated CO2 if lighter skin.