From what I've read about computer engineering, it is more similar to computer repair than anything else.
In most universities I looked at, ECE is the norm: Electrical and Computer Engineering. So CE is engineering and under the broader ECE, not EE.As for seeking advice, NEVER talk with a general counsel about your future or even course choices. They are all drones! Go to the department, ask front desk to speak with a professor, like me. We know a lot more than a counsel, which (see the drone analogy?) will point you in the wrong direction way too often and is not trained to do any degree-specific advising. Once one of them drones told a student interested in a physics class not to choose a certain class because "Astronomy 106 is TOO advanced for you!". Come on! It is a 100-level class! It's for first year students, where is "advanced" coming from, his personal experience?! Damn those drones!
Read my location. I'm in a public school, predominately undergraduate institution. A student doesn't have to be very competitive to get in. We look at 6-year graduation rate, instead of 5-year for the big research-one universities. I usually see students over-schedule themselves when they have 16 undergraduate credits and hold 20-30 hours a week job(s). That is not possible. Working minimal wage jobs isn't going to pay for college tuition, just making college a few years longer. If you can afford to go to college without working, borrowing from government and parent is fine. You get to graduate earlier and start making enough money to pay back.
@Liudr sounds like a professor i'd spend most of my days picking his brains on what he knows.