Probably not. Each state has their own definitions of who is in what phase. The national government sets standards but states can do what they want with their allocation.
Are you in Texas? Obviously Phase 1B has either started in Texas or will soon start, depending on who you talk to. Phase 1B in Texas is bigger than 1B nationwide since it goes down to age 65 and includes ages 16-65 with certain heath conditions. I think 1B covers about 1/3 of all people in Texas,. Covering obesity added a big pile of folks to the list. Other states have a narrower 1B so they will transition to 1C sooner.
Within Texas, the vaccine allocation has been pretty equitable across counties. The Pfizer vaccine requires cold storage that some counties don't have, but maybe they are getting more Moderna. You don't have to be vaccinated in your county or even your state, so hunt around if you really want it.
I would guess that Phase 1B in Texas will be winding down .... sometime in March? I base this on Fauci and others saying that willing people will have access to a shot by June or July, so by March we should be at least 1/3 of the way to that goal.