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

I agree that the "pumping" answer seems odd.  With an experienced injector,you should not experience this. Botox itself lasts for around 4 months and treating crows feet should not generate fluid collection in the lymphatic under the eyes.

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.