It is a great idea to ask around at you school or your office for recommendations on where to go for each specific malady you are troubled with.
If you can, go to the actual hospital with someone who speaks Japanese. If you can`t find anyone, there is a searchable database run by the prefecture for finding an English speaking facility. You can select various criteria such as location, language and service. Local pharmacies can also be found here. Please call ahead to find out if the information on the website is accurate: confirm what time they are open, the location and whether or not there is actually English speaking staff there.
(http://www.e-navi.pref.miyazaki/lg.jp/qqport) Then click the button written in English. This will bring you to the search page.