Is entropion caused by Botox? (Photo)

It seems like you are concerned about upper eyelid hooding.  There is a sort of tug-of-war between the muscles that lift the eyelid and the muscles that depress it.  Botox relaxes and temporarily weakens the effect of the muscle.  Depending on where and how much the botox is placed effects the tug-of-war, and will either contribute to lifting or depressing the eye lid.  In general, injecting the outer frontalis muscle depresses the lateral lid, while injecting the muscles that create the crow's feet (obicularis oculi) muscles will open up the eye a bit.  

Entropion is an inversion or rolling in of the eyelid - generally the lower lid. I have never heard of it from Botox, which has been reported to cause ectropion (the reverse, the lower lid rolls outward exposing the moist inside lining). I did not see either ectropion or entropion in your (somewhat limited) photos.  From your captions, it seems what you are really noting is a lowered brow and lid on one side. Brow descent can be caused be Botox injection in the lower forehead. The brow position in this case may be able to be improved with additional Botox in the orbucularis oculi muscle, which pulls the brow down. The effect will wear off and the position normalize when the Botox wears off in 3-4 months after injection. The undesired effect should be considered for injection location in future treatments. 
I hope this is helpful. Good luck.

In these pictures there’s no evidence of ENtropion , a botox treatment could cause ECtropion in the lower eyelid only in selected case and bad use of toxin and his inoculation site. 
I can only suggest to wait, botulin effect could last much more than 6 months. Vitamin B complex and alpha lipoic acid could help nerves metabolism to increase recovery processes. 

Entropian is a condition of the lower eyelids. I can't tell from the pictures whether you have entropian. Botox can cause ectropian of the lower eyelids, but I am not aware that it can cause entropian.