Is my two-way switch installation easily fixable?
Look at the other switch; there should be 1 coming in; a black live, and 2 travelers black and red or black and labeled black coming out. The neutral will just be pigtailed. If there is just a single switched live going out then you will need to run an extra wire to the other switch.

To make a single switch into 2 you need an extra traveler (switched live) between the switches.