Can Botox Cause Water Retention Under Eyes?

Botox does not cause swelling. And, unless it is very dilute, there should not be much saline either. Additionally, the small amount of saline used with the Botox should be absorbed with in a few hours at most. If you provide pictures, we may be able to give you more advice.

This is an uncommon complication but I have seen it before. I would massage and it should resolve in a couple of weeks. If not , you may have to deal with it until the botox wears off.

The fact that the lower eyelid became puffy one week after your Botox injection makes me doubt that this is due to edema. I suspect that this "bag" could very well be from pseudo-herniation of the obicularis oculi muscle due to the botox.
When the obicularis oculi muscle is flaccid, it bulges out, just like when you are really tired. If Botox is the source of your problem, it can take up to 8 weeks to resolve.
Swelling and edema are less likely and should resolve within a week.

In some cases, too much Botox around the eyes, or in the wrong spots, can cause temporary (three months) puffiness under the eye. The Botox weakens the orbicularis oculi muscle, which surrounds the eye in a circular manner. When this "squeegee" muscle is made too weak, it can't squeeze tight enough to squeeze excess fluids out from around the eye.

Lying down on your pillow allows gravity to increase fluids around your eyes. In the morning, we normally wake up with slightly puffy eyes and throughout the day blinking improves it. Botox could possibly inhibit this action. It should improve as the Botox wears off normally over 2.5 to 4 months.

Botox does not cause swelling. you  may have malar edema which is like having swollen calves.  This is very difficult to treat.

Fluid from the forehead or glabella (between brows) can travel with the pull of gravity to an area of least resistance, in this case the lower eyelid. I would recommend gentle massage of this area to encourage fluid to leave the tissues in that area. I have seen fluid of the lower eyelids last 2-3 weeks.