Rash under my arms after Botox that would go away within 4 months and reappear after each injection. Should I try Dysport?

One unit of botox, even the dysport equivalent is a very very small amount. It is most likely the placement/area in which they injected the second time, but I would consult the injector who did the second treatment and let them know about your issues. 

A small amount of neurotoxin, Botox or Dysport at the border of the lip can create a slight lift but not additional fullness.  It can also relax the vertical lines above the central lip border.  

Alcohol before or after injections is not recommended as it can thin your blood and increase your risk of bruising. However, it will not alter the outcome of the Dysport and is ultimately up to the individual. Be sure to discuss pre and post instructions with your injector. 

Causes include a low brow,injection near the brow,injecting the frontalis muscle but not the corrugators,overactive lateral orbicularis muscles,effect on the levator muscle.See the doctor who treated you to determine the problem - eye drops can help a levator problem.

With cosmetic dosages of Dysport it is highly unlikely to develop systemic side effects such as tachycardia.  I would seek an evaluation with your primary medical doctor to rule out other possible causes of these symptoms.  

Thank you for your question. There are no contraindications between most Augmentin and Dysport.  I recommend having a follow up with your doctor. Hope that helps. Best of Luck!