> Would I upload/integrate my public key?
I presume this is a typo, but if so it's a grave one.
The naming is very transparent, the intent is that we can give everybody our public keys, they're public, while our private key must remain secret.
(I like to use the U2 Lyric "A secret is something you tell one other person, so I'm telling you" to keep straight the difference between secret keys, which we must share with somebody else, and private keys, which we shouldn't share with anybody, although DH means in practice you may never need to explicitly "tell" anyone the secret keys in hybrid systems)
[Edited because I made the same dumb typo]