Puffy Under Eyes After Botox?

There are several possible reasons for this:
1) Swelling from injection fluid/volume: I don't believe this is your problem because it should be resolved by two weeks after your injection.
2) Lymphedema: This is a more likely possibility. When your muscles move, they pump fluid out of the area. For example when you stand still fluid can "pool" in your ankles and you need to walk to get the muscle pump working to move the fluid out of your legs. This sometimes happens around they eyes.
When you lay down at night, your head tends to have more fluid in it. This can be seen by the distention of your neck veins (called Jugulovenous distention). Generally, your eyes are more swollen in the mornings due to this. During the day, gravity and your muscles (eyes blinking) tend to pump that fluid out of there. With Botox use in patients with a lot of lower eyelid and crow's feet wrinkles, the weakened action of the muscle can contribute to diminshed pump action of the muscles.
3) Diminshed muscle tone (paresis): This is the most likely cause and is a double edged sword. The weakness of the muscles diminishes the wrinkles but it also weakens the ability of your eye muscle resting tone to hold back the fat within your bony orbit. I know that sounds complex but let me simplify with an analogy.
It is not uncommon for individuals to have a resting abdominal muscle tone that "sucks in their stomach". If I were to sufficiently weaken your abdominal muscles then your abdomen would bulge out due to the organs contained within. The same goes for the eyes: sufficently weakened eye muscles cannot contain the fat around the globe and it tends to bulge out the lower eyelid.
I apologize if that is oversimplified. I hope this helps to explain.

All good information. We would like to suggest, however, that any massage or manipulation should not be over zealous as this may exacerbate the problem.

We also believe that dosing with Botox or Dysport under the eyes into the eye muscle (orbicularis occuli) should not be done beyond the mid-pupillary region for almost all patients.  For the  majority of patients, dosing even further away from this area is prudent and still offers excellent outcomes.

Thanks for your question -
There are several excellent answers posted below - I'd like to explain in a bit more detail what is likely happening in your case.
It is unlikely that the swelling is due to the volume of the fluid or edema injected two weeks after treatment.
It is much more likely that there has been a moderate amount of paralysis to your orbicularis oris muscle. This muscle is circular and sits on top of your bony orbit. Paralyzing the muscle can cause increased promience of undereye troughs as the muscle tone helps keep this area tight.
It will require time to allow the botox to wear off.
I hope this helps.