My laptop does not have a built-in ethernet port because it is new so I used to SSH with my pi via a USB-ethernet adapter but I recently went to Russia and forgot the adapter in the US and since I am in Russia, nobody sells such adapters and when I did find one, it was a fake Apple adapter made by ASIX which was cheap but did not work due to driver errors.
My only option now it seems is to use a USB-USB cable for connecting to my pi and I just want to know if it is possible.
Unfortunately not. There's no protocol to connect computers by usb. But there are a lot options to connect PI by wifi (for example making access point by your Mac).
Edit: Now i see "putty" tag. So i think that youre not using Mac. Despite it you can still connect Pi and your PC by connecting to the same wifi net (for example your phone hotspot)
I know this is an old question but the solution is even older. Male to Male USB bridge networking cables. See the article(from 2005) for a better explanation. Amazon has plenty of similar, if not the same, cables available at the time of this writing(12/2018). While it's not the exact solution to the question I thought I'd add this so future users can be made aware.
Connecting Two PCs Using a USB-USB Cable(November 16, 2005):
https://www.hardwaresecrets.com/connecting-two-pcs-using-a-usb-usb-cable/
