You can bring any prescription medicine into Japan without any special procedures on the condition that:
(1) you bring it only for your own use
(2) it is not a prohibited drug such as methamphetamines
(3) it is not an illegal narcotic
(4) it is only a one month supply
To bring more than a one month supply of prescription medication with you to Japan, you will need to acquire a form know as a "Yakkan Shoumei". The procedure for acquiring this form can take a couple of weeks, so please do take care to do this well in advance of your trip. Full details concerning this form can be found here: www.mhlw.go.jp/english/policy/health-medical/pharmaceuticals/dl/qa1.pdf.
Contact lenses can be brought to Japan, but in no more than a two month supply.
Cosmetic items can be brought to Japan, but there is a limit of 24 per one type of item e.g. 24 lipsticks (regardless of brand, colour).
Further details can be found on this website: www.mhlw.go.jp/english/policy/health-medical/pharmaceuticals/01.html.