Eh, it does not sound like you thought this through. I would prefer my medical data to reside in my country, so that its governed by privacy laws I vited for.
The whole blockclain free-for-all ungovernable banansa has it's place, but its not for everything.
It sounds like you live in a country that is not Pakistan, where it's likely to make more sense for tech companies to operate within the system rather than staying outside of it. Even so, it would ultimately be up to you whether to trust any specific company with your "medical data", with one of the factors being whether they were bound by your country's legal system or not.
And who mentioned anything about blockchain? The philosophy of routing around censorship and end user empowerment is much older than blockchains, and that you're pigeonholing the ethos as "blockchain" just shows how much we've forgotten.
The whole blockclain free-for-all ungovernable banansa has it's place, but its not for everything.