Is it an emergency to have inability to open wide on my tmj?

Not usually.: It would only be an emergency if you were having trouble breathing and needed to be intubated by a doctor. It's very common to be unable to open your mouth wide with TMJ problems.

It can be: If this just happened rcently, go to your dentist and seek reduction of the problem. If long term you might need the services of an orthodontist or oral surgeon for definitive care.

Not necessarily: Depending on how sever your locking and the associated pain with it, it is not necessarily an emergency that needs immediate attention, but waiting can make things worse. Having a closed lock (limited opening) of the jaw can be very painful and create a lot of anxiety and compromised eating, talking and functioning. I would try and see a dentist and/or tmj/tmd specialist asap.

Maybe: Depends. If you have acute pain. See an oral surgeon ASAP. If it is not painful, ok to wait a few days.