Too Much Botox Injected on Area

You definitely want to make sure you are getting treated by a licensed medical professional. Although Botox is a non surgical alternative, you do not want to let an amateur inject your face with this solution.  Too much Botox can lead to drooping of the eyebrows.  Other more serious side effects from Botox include symptoms consistent with botulinum toxin effects.  If you have not experienced generalized muscle weakness or urinary incontinence and breathing difficulties, you should be just fine.  In the future, however, I want you to be careful where you get your Botox done.

If your practitioner injected too much Botox, the only likely side effect would be eyelid droop if he/she injected in the forehead or brow area (between the eyes included).
When too much Botox is used in this area, the effect is to relax the facial muscles too much causing the brow and eyelids to appear heavy and droop. This will usually resolve within several months but in the meantime there's not much that can be done.

Finding a physician to perform Botox procedures is extremely important as the marketplace becomes saturated with physicians and paramedical staff performing the procedure.
In your particular case, it is reassuring that you have found a physician who is undoubtedly honest and trustworthy. Mistakes can happen even in the best situation, but the approach your physician took to explain the situation to you is commendable.
Experience is absolutely necessary in acheiving optimal results with any cosmetic procedure. I would advise going to a Board Certified physician with extensive experience in the field of aesthetic rejuvenation.
The long term effects of the botox injection are trivial as the product is temporary and will dissipate with time.