Games : Login to minecraft without ability to connect to minecraft.net

So, I have a copy of minecraft.exe file on my school drive, but the school computers have some restrictions. First of all, I need admin to modify anything onto the physical drive. I can only access a removeable drive, stored on a remote server, as a Z: drive, and it is connected when I log in to my personal account. The main obstacle however is that minecraft.net is blocked. I downloaded the launcher by pushing it through google drive, so I have that much. I do have a valid mojang account on which I paid for minecraft. But since minecraft.net is blocked, when I log in, it returns an SSL connection error as it is unable to connect to minecraft.net which is a blocked site. Is there a workaround? Does mojang own other servers that store user accounts that would not be blocked?