No, putting Rogaine on one area will not cause other areas to lose their hair. Most commonly there is some shedding in the immediate area it is applied temporarily, before stimulating more growth in general.
Yes, alopecia areate can be limited to the eyebrows. A steroid injection can help resolve this situation in many but not all individuals. One should not inject a high concentration of steroids for alopecia areata because this can cause depressions of the skin.
If you want to know how to treat your hair loss and the best approach, see a good doctor experienced in this field. Good doctors do not make such recommendations over the internet that are not customized to your individual needs
