The reaction that you are describing is not a known side effect of Botox. It is possible that you have an eye infection that occurred at this time which is unrelated to your Botox injection. i would advise you to consult with an ophthalmologist to rule out an infection or other cause of your eye problems. Please let me know what happens.
There is no really good reason that would link crusty red eyes with Botox. Perhaps you have a case of conjunctivitis. You should see your primary care doctor and have an exam. Cotton compresses with warm water can relive some of your symptoms if you have a viral conjunctivitis (most common), but if it is bacterial you may need eye drops so it is important that you notify your primary care doctor that you are having this problem.
It sounds like you may have conjunctivitis - usually a viral or bacterial eye infection and less likely an allergy. It is likely it is just a coincidence that the symptoms began with two weeks after Botox. Conjunctivitis is sometimes very contagious and may be passes easily among kids and adults. I would get your eyes checked by your primary care MD or an ophthalmologist ASAP. It would be rare for Botox treatment to cause conjunctivitis, esp. if clean/sterile utensils are used and alcohol solution was used to cleanse your skin before treatment.
The reaction that you are describing and the treatment recommended by the doctor sounds like seborrhea of the eye lashes. Has no relation to the Botox injections at all. Only coincidence.