I’ve already sent my deposit to another university in April, but due to a change in financial status, paying for that private university would be a challenge as I received little aid. I was accepted to UCSB but is it too late now (June) to change my mind and see if I can go to SB instead of the other university?
The people that know work in UCSB admissions. Every day you wait after posting here before calling the people who can actually decide to let you or not is a day the chances go down.
Exactly as @mikemac said – get off CC and call UCSB right now. 
Good luck!