When Will the Swelling, Puffy Eyelids Go Away?

Sometimes after Botox people complain of "swollen eyelids." This is most likely not swelling. It is because the Botox was injected too close to the eyebrow. It is no surprise that this happened 8 days after your injection, since this is when the Botox had finally started working (it takes 3 to 7 days for the Botox to take effect). The eyebrow then drops (ptosis) and the skin between the upper eyelid and the eyebrow gets compressed into a smaller space - the distance between the eyebrow and the upper lid become shorter.
This makes the upper lid skin puff out since it has nowhere else to go. So, I would recommend looking at your pre-injection photographs and compare the level of your eyebrows. There is no solution for this except for time - 3 to 6 months for the Botox to go away. This most often happens to patients only the first time they have Botox.
It is very difficult to predict which patients will have this response. If you do have this response, then you will know the next time you have Botox to have it injected higher above your eyebrows. This is a compromise, since you may be left with a wrinkle above your brow, but that is better than the dropped brows.

It sounds like either one of two things is going on:
1. At around 8 days you achieved the full effect of Botox. When injected incorrectly it can cause a heavy or drooping brow which may look and feel like swelling, but is related to the brow moving downward which creates unusual pressure on the eyelids and eyes.
2. If the Botox was injected correctly, it may be that your symptoms are unrelated to the Botox injections.
In either case, we suggest a visit to your practitioner to be evaluated. Good luck.

The swelling around the eyes related to Botox injections 11 days ago could be related to where the Botox was injected. Steroid pills may help with this, and a low-salt diet would also help. Cold and hot compresses 11 days after the procedure was performed will not do any good at this point.