This is a common side effect of taking cortico-steroids, which is basically taking adrenaline. For most people who get an anxiety reaction from them, it goes away when they stop taking it, but some will internalize the thinking process caused by traumatic events (or I should say, the brain does this for reasons we don't understand yet) and the problem can become chronic. Kind of like PTSD, in a way. If this sticks around much longer, I'd go see a therapist who specializes in anxiety treatment who can rewire your thinking back to what it was, hopefully. Meditation and exercise might help get you back to your normal self. Just knowing this is common and usually does go away I hope will be of comfort to you. Sometimes, trying to figure out why the doctor gave you the drug in the first place can help you get your mind on something else -- did he or she see inflammation, or was the doctor just guessing and picked a drug out of his drawer? Vertigo can have a lot of causes, and inner ear problems are one source, but the only way a cortico-steroid helps is if there's inflammation -- it is a very good anti-inflammatory. But the side effects are well-known as well. Good luck, relax, this probably will pass, most likely your mind is hanging on to this because the experience was intense and unexplained.
Did the vertigo stop? Being sick for a prolonged period makes a person both anxious and depressed because you might wonder if it will ever stop.