Dermatologist used Botox along eyelash line instead of Lidocaine to numb area before removing skin tags.

No physician would knowingly use Botox instead of lidocaine for numbing. There are two muscles that work on the eyelid. One closes the eye, the other opens it. In your case, the muscle that closes the eye is likely weakened (In fact, we sometimes use Botox to weaken this muscle for people suffering from eyelid spasms).  It is important to lubricate your eyes. The good news is that Botox effect is temporary, lasting up to 3-4 months. Discuss with your physician and consider seeing an ophthalmologist or oculoplastic specialist.

I often place botox along the eyelid margin for patients with blepharospasm associated pseudo-apraxia of eyelid opening.  Only rarely will it cause ptosis.  However, botox placement around the eyes does weaken the orbicularis muscle, which closes the eye.  Therefore if it is weakened then it will temporarily cause diminished eyelid closure and drier eyes.  If your having problems I would see an optometrist or ophthalmologist.  Most patients do well with an over-the-counter artificial tear like "Blink" or "Systane" or "Genteal."  I've included a reference I published on use of botox along the eyelid margin for the "apraxia" --difficulty of opening the eyes.  I would expect your dry eye issues to clear up pretty quickly (probably within 6 weeks).  Best regards.  

 Obviously the Doctor placed the Botox in the area by accident thinking it was lidocaine. This should wear off but may take months. I would visit an ophthalmologist for recommendations on a topical re-wetting solution or ointment. The ophthalmologist will also probably advise you to tape your eye closed at night so that you don't develop dry eye and corneal irritation problems.