Be careful, in the past 10 years or so AZ has cut funding to its universities by more than 50% (the most in the nation by far) and is now considering cuts to its Liberal Arts programs. Nothing is certain on the matter yet; the extent and targets of the cuts aren’t known but are likely to hit political science, history, etc.
So, do apply to Barrett as well as to UA Honors (they take Spring transfers in fact), but diversify your application list.
If you’re at a commuter AZ branch campus, I can understand why you wouldn’t have the proper level of challenge nor a sense of community.
The second issue will be financing: did you save $$ by attending your current college and if so can the money now be used where you transfer?
Research and demonstrate interest at various colleges known for their academics even if they’re not T20. For instance, Pitzer, Occidental, Whitman have excellent financial aid and academics. Emory, WashU StLouis could be on your list.