A bad asthma attack most certainly CAN make you feel breathless throughout the entire day and for several days at a time. In a severe episode of asthma you may not just have acute bronchospasm but inflammation that is persistent. Add to that your anxiety, no doubt that's making breathing more difficult and they are affecting each other. It's scary and it can be hard to break out of a loop like that, but worrying that there is another sinister diagnosis going on at this point is going to be of no help. You're on good strong medications, trust that they are going to do their job, but also know that they are going to take a few days.
Steroids can make you feel a little loopy sometimes, they are known to do that but they are good meds for asthma. take it easy for a few days and let us know what your doc has to say