I would go in for your appointment this morning and ask both the nurse AND the allergist doctor about your experience. It doesn't sound like an asthma attack, but it DOES sound like an allergic reaction that compromised your respiratory system. If you were given an epi-pen, it's because they knew there was a possibility of a reaction and I'm sure they knew you had asthma which greatly increases the severity of a reaction and makes your airway close much faster.
If you had used the epi-pen, you would have had almost immediate relief from the coughing and respiratory problems because it reduces the swelling of your airway. It is basically a shot of adrenalyn and is harmless so don't be afraid to use it if this happens again. It buys you the time you need to get to the ER. You still need to go to the ER even if you do feel much better because they will want to monitor you once the epi-pen wears off and make sure you aren't going to head back into anaphylaxsis.
They should have been very clear about why you were given the epi-pen and how/when to use it. I'm sorry you had such a scary experience - we've had LOTS of asthma attacks and allergic reactions (severe peanut allergy) between my son and myself so we know all too well what you were going through. Go in this morning and ask questions of everyone BEFORE getting that shot again!