After using my inhailer my hands start shaking. Is this dangerous?

No. I imagine that you are talking about an albuterol inhaler. This is not an unusual occurrence. Albuterol (the drug in proair, ventolin, and proventil) is a beta agonist. This means it can activate part of the sympathetic nervous system, the fight or flight system. Some docs will offer you xopenox, another similar inhaler, because some feel that it causes effects like this less often. It is very $$.
Not likely. A common side effect of albuterol (i'm assuming this is the type of inhaler of which you speak) is elevated heart rate and tremulousness. Usually this is not dangerous but the use of albuterol should be limited to only as needed. If this is bothersome or causes blood pressure to rise abnormally you could have your doctor change your inhaler from albuterol to xopenex (levalbuterol).