Yes there are restrictions. Injections that are not auto injectors you need Yakkan Shoumei for the syringes.Re: Japan, I just spent a few days there and they checked my luggage at customs. They only cared about narcotics, benzos etc. There was no issue whatsoever with injection supplies, T cyp or HCG. This was consistent with the published information I found regarding Japanese regulations for meds for travelers. Their "controlled" and "illegal" drug lists do not include TRT meds and state injection supplies for a month are allowed.
Ministry of Health, Labour and Welfare: Information for those who are bringing medicines for personal use into Japan