First, I am NOT a doctor, but a fellow sufferer of hemiplegic episodes as well as asthma.  My foremost recommendation, in light of the fact that your episodes are exacerbating your asthma is that you discuss this with both your pulmonologist and your neurologist and ask flat out "are my episodes a medical emergency or can they be safely treated at home?"  Your doctors are the only ones who really know your particular case and can answer that accurately.  And asking separately of both specialties means covering all your bases, because a great neurologist may not know a whole lot about asthma (and vice versa). 

I have full-blown paralysis during some of my episodes, but my docs are actually okay with me not rushing to the ER for every attack.  The exceptions are if the paralysis affects my airway that time, or if I somehow physically injure myself as a consequence of its sudden onset (possible concussion or whatnot).  It's similar to the "rules" about whether to call an ambulance for a person with known epilepsy having a seizure.  Bottom line:  your docs should be able to tell you what is hospital-worthy, what merits a phone call to the dr's office, and what you can just keep track of and report at your next appointment.  Until you know for sure?  I'd say err on the side of caution especially if you're having trouble breathing!!!