usually the prozac will cover the withdrawal from lexapro, but apparently not in your case. the most important fact is that you are getting better which means it will keep getting better, there is no relapse, so you will just have to stick it out.
Most likely yes, nobody knows how long it'll last because we each respond differently. Going cold turkey is not a good idea, even when switching from one med to another -- no med is an exact equivalent of another. It sounds like you're getting better and hopefully you'll be fine soon; if it gets too debilitating or emotional you can go back on the last dose of Lexapro at which you felt fine and taper off slowly. I'd also switch psychiatrists.