A wide variety of medicines are available in Japan, including most common over-the-counter ones such as paracetamol, ibuprofen and aspirin. Hay-fever/allergy medication, contraceptives, lip balm, specialist soaps, skin treatments and more are also easily available.
Pharmacies, known as kusuri-ya (くすりや) in Japanese (literally "medicine shops") are everywhere. Most sell both medicine and various health and beauty products. All the labelling will be in Japanese, but items like soap and shampoo often have some English text on them. Pain killers tend to be entirely Japanese though, so it may help to ask staff for assistance. You can of course bring your own supply of things like paracetamol and ibuprofen to Japan as there are no customs restrictions on small amounts for personal use.
The main form of contraception in Japan is the condom. The contraceptive pill is not widely available or widely used. The morning after pill is available in emergencies but rather expensive. You can bring your own as there are no customs restrictions.
Note that Japanese condoms tend to be a bit smaller than typical western ones, so you may need the "XXL" size (which isn't really XXL, just slightly larger). Love hotels provide condoms, but only the standard size ones.