To visit a doctor, you don’t need to register but you will need to call for an appointment. It’s best to get your hotel to call for you.
There is a list of doctors who are advertised to speak English, but generally it’s best advised to speak slowly with basic expression.
We did find a doctor in Asakusa who spoke English and French but we still needed Google to explain some things. Our recommendation is Kotobuki clinic, albeit they specialise in respiratory problems and their site is in Japanese- get your hotel to call for you and explain your symptoms!
Their treatment may also surprise you. They may ask you to use a oxygen mask and the strength of medication may be weaker than what you are used to. In our case, for a viral infection, it seemed to be penicillin and a variation of pain killers, but nothing is written on the box. Whatever it was, it worked, so that’s the important thing. The receptionist couldn’t speak any English but we managed with some Google and hand gestures.
It seems a doctor in a local clinic will be cheaper than one installed in a hospital, so choose carefully!
For our doctor in Asakusa, finally, the pharmacist was just down the road, and she spoke French! The cost for the medicine and treatment was around €60. And most importantly for our personal experience, the problem (fever and pain) was cured, at the cost of a day in rest.
Not vouching for the others, proceed at your own risk! Stay safe, traveller!