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Speaking to a medical doctor isn't necessarily confidential. I believe there are some categories of things that doctors must report to authorities, and that varies from US state to state.

Wikipedia says: "In the United States, the Federal Rules of Evidence do not recognize doctor–patient privilege."

Would it help if I buy internet access from my lawyer?

But not if you're speaking to them over the Internet.

Right. If you're doing that, I'd recommend making sure that the tools you're using to communicate with them can encrypt your messages and their messages using some protocol that only the intended recipient can reverse. Public-private key encryption seems to generally be a good approach.

Look for the "padlock" icon in your browser before talking to your doctor about Viagra. ;)

Even off the Internet, the fact that you talked to your lawyer isn't necessarily protected even if the content of the conversation is.

Add Priest

Only if you're a lawyer... and you're their lawyer... and you're talking about their legal matters.