Be very cautious about Rogaine!
From a useful website;
Dermatologists often suggest trying Rogaine to help hair grow back after chemo treatments, including Taxotere. Doctors usually recommend a maximum strength formulation of minoxidil, the active ingredient in Rogaine, which is marketed to men. But Rogaine comes with a really big drawback. You have to use it twice a day, every day, for the rest of your life. Stop using the drug and your hair will fall out.
Best to get professional advice - hair loss can be upsetting but for most women it’s temporary.