I have signed into two Google accounts and would like to switch account in Google URL shortener site. But currently, there seems no way we could achieve that.
The normal "switch account" option is not currently available with goo.gl. Here are some workarounds.
Either sign out of all Google Accounts, then sign in with the account you want to use
Open a New Private (Firefox, or Incognito with Chrome browser) Window, then sign in only with the account you wish to use with goo.gl
If you are using Internet Explorer browser then use InPrivate Browsing. (Gear/Settings | Safety | InPrivate Browsing)
Close the private window to return to your previous pages.