I don’t know how much you know about ECB at UT, but you name-checked it so as a current student I’ll talk about it a bit
There’s no combined major for those two programs–there’s an honors program. It’s extremely selective and one of the best values out there; you get Canfield (business honors) and ECE honors. ECE honors is extremely difficult with respect to its workload, and I’m sure it’s more difficult with Canfield on top of it. I think you’re competitive for UT out-of-state, but I do hope you realize that shooting for one of the most competitive honors programs at a very competitive university, with a cohort size of like 30 out of 10k (and when applying for ECE you can apply to several I think) will be difficult. Good luck! https://ecb.utexas.edu