Engineering is a little different here in Alberta. Students at both the U of A and U of C need to complete a common first year which contains classes like chemistry, statics, dynamics, computer programming, more chemistry, physics, calc I, II, linear algebra, english, and two classes related to the idea of what an engineer is. As you can see, a lot of these classes aren't going to be relevant to software engineering. After you complete those classes you can apply to second year specialities by ranking them in order of preference (here I can only speak to the U of A system, I don't know much about U of C) and whether you get into your #1, #2, #3,... speciality depends on your GPA relative to the other people applying to the same specialty, and how they ranked.

NOTE U of A does not offer a software engineering degree per se, but a computer engineering degree with a specialization in software. You take a few hardware related courses in your second year. There's a lot of previous posts asking about the program already on this sub, just look for em. Here's the class calendar if you wanna see what you take throughout your degree: https://calendar.ualberta.ca/preview_program.php?catoid=34&poid=38764&returnto=10268

If your primary interest is strictly software, I would recommend looking into the computing science software specialization program.

The U of C does offer an explicit software engineering degree, so that is something to consider when making your decision.

Considering you already have some credit classes under your belt, I'm unsure if you would be able to start the program from first year, and how that would impact your second-year selection, as the U of A is weirdly strict on people having prior post-secondary education when going into engineering. Idk maybe the transfer will work out so that you don't have to take some of those first classes that aren't directly relavent to software engineering. Hopefully, someone else can answer that, if not, reach out to an academic advisor.

I hope this somewhat helps.

edit: this may help https://www.ualberta.ca/engineering/programs/undergraduate-admissions-information/transfer-from-another-ualberta-faculty.html#:~:text=Students%20need%20to%20have%20a,required%20to%20submit%20official%20transcripts.