My jaw keeps clicking when I try to open my mouth. It feels off- is this trismus (lockjaw)?

No. Trismus just means that it is difficult to fully open the jaw and usually has nothing to do with "lockjaw' which is the term for tetanus infection causing muscles to seize up. Jaw clicking is more likely to be caused by problems in the tmj- or jaw joint. See you dentist or a maxillofacial surgeon to be evaluated.
Disc Displacement. Disc displacement with reduction is usually not accompanied by pain indicating that most patients are able to adapt to the dysfunction.
No. The clicking is most likely due to a displacement of the cartilaginous disc located between the condyle (ball) and socket of your tmj. If the disc is dislocated anteriorly it will reduce when you open and make the clicking sound. It usually clicks again when you close as the disc displaces forward again. You should see a dentist that treats these problems specifically.
Jaw disk malposition. Having popping/clicking TMJ noises not necessarily a problem. Many people experience these noises. Without pain or limitation of function the noise itself is not an issue. If you have locking or limited movement, "ear" pain, headaches, morning jaw stiffness/soreness, difficulty chewing, bruxism, previous jaw injuries or other jaw conditions, the problem is more serious. Then see a TMJ specialist.