What approach should I take against an ER doctor who, after informing him of my asthma, gave me a medicine whose side effect is “can cause asthma”?

Why would you take any approach against the ER doctor?  Were you injured?

A medical malpractice case requires four elements -- duty (what a reasonable ER doctor would do or not do under the same circumstances), breach (not doing what a reasonable ER doctor would do), damages (i.e., an injury), and causation (the breach caused the injury).  Proving these elements requires expert testimony (hence, it is expensive).  Many states (including Florida) have special "pre-suit" tasks that must be completed (hence, it is expensive) before you can file suit.  To file suit requires a lawyer (hence, attorney's fees).  To win a malpractice lawsuit requires several legal procedures (which all cost money in addition to attorney's fees).  You can see that a malpractice suit is not cheap.

In the end, your damages will have to pay all of the expenses, including attorney's fees and re-paying your insurance company for your medical bills.  Most states (including Florida) have "caps" on the damages you can recover.  Only after all of the expenses are paid out of the capped damages will you get any money. 

This is why good malpractice lawyers turn down most malpractice cases.  Even if there is malpractice, the potential damages have to be high enough to recover something that actually benefits the injured patient.  If you do not have damages, you have no case at all.  If you have minimal damages, it will not be worth your while to bring a case and most (dare I say "all"?) malpractice lawyers will decline to bring the case. 

If you have very significant injuries and damages, I suggest you consult a medical malpractice lawyer in your area.  If you do not, I suggest you forget about this and count yourself lucky that you were not seriously injured.