Browneyes, first off, calm down and take a deep breath. I know it's so easy to panic, but the stress *will not* help your hair loss situation. Your low ferritin level is an absolute flag, and low ferritin, especially as low as yours, can cause Telogen Effluvium. This is good news for you, and let me tell you why. As long as you start treating your deficiency, you have a very good chance of getting regrowth. Telogen Effluvium can be reversible if you remove the trigger that's causing your hair follicles to go into resting state.
Sometimes Telogen Effluvium can mimic Androgenetic Alopecia. That was the case with me. At first they thought I had Androgenetic Alopecia because I had a lot of hair loss on top of my head. But, I am starting to see some regrowth, even though the shedding hasn't stopped (in my opinion) in the shower. So, be patient and treat the iron deficiency first, because if you can take care of that problem, then you will be in a better position to assess if you have Telogen Effluvium and/or Androgenetic Alopecia.
You may want to hold off on using Rogaine and first work on your ferritin levels. This way, you will know if it's the low levels that are causing your hairloss. Once you either confirm or rule it out, then you can explore Rogaine as another option. If you move forward with Rogaine, it's okay too if that's what your derma told you to do. But, you won't know if the regrowth or lack of shedding is due to you raising your iron levels, or if it's due to the Rogaine. You need to decide which way you want to go based on this.
Good luck to you and calm down. I swear to you, stress makes the hair loss worse (I've experienced this personally), and you don't need to add to the vicious cycle. You're going to be okay, Telogen Effluvium is not a bad thing to have because you can recover from it, and you're also very lucky because most women don't get a positive test result that flags a deficiency that can be reversed. There are a lot of women out there who get all normal test results, and then they don't know what to do next. You have an inbalance that has been proven by medical science to cause hairloss, so now you can do something about it.
Be patient, it will take several months before you can see anything, but have faith that you're taking care of the trigger, and keep getting your levels tested until they come back to normal. Only then, will you be able to make an assessment about where you are at with your hair loss.