There is a lot of reasons for hair loss in women population. The description you gave is indicating that the most probable cause is Androgenetic alopecia - because it happened after delivery. You should visit the dermatologist and do the conventional blood tests, check the Ferritin, your hormonal status in order to get the adequate therapy.
Your skin should get back to normal in 7-8 days. By the experience in my practice we have concluded that the possibility of Allergy or intolerance appearing is pretty much tied to a Brand of the Minoxidil manufacturer. If your allergy symptoms are high, you should take some antihistamine (first, of course, consult your doctor) in order to lower the effect of Allergy.
The difference of using Rogaine once or twice daily is not so big. It can be more effective up to 8% if used twice a day. I would advise using it in small dosages once a day in the evening, in order to have the possibility to increase the dosage later.
One month after the procedure you can relax and act like you had no hair transplant. In other words, feel free to wash your hair as you used to, the grafts have adapted to the new area completely.
5% therapy is a standard dose, and it is giving the good results. There is no reason to take the stronger therapy.