hi! for me, when the semester starts i go through all of my syllabi and write down all of my assignment due dates on my notes app (usually notion, though this semester i'm trying out a new app) as well as exam dates. it's definitely tedious at first, and maybe even overwhelming, but once you have those dates written down and easily accessible, it'll make keeping track of stuff better. alternatively, if your college uses canvas, i hear you can export assignments directly to whatever calendar app you use - i haven't tried this myself yet, but i'll give it a shot when my own classes are put up.
also also, cannot emphasize this enough, use your college's resources!! you're probably playing a shit ton of money in tuition and fees, might as well make it worth it. i was doing not-so-great during my first year, and my english professor referred me to the university's learning center and it was the best thing that could have happened to me. the person there helped me connect with other resources, and guided me in having a better handle on classes. so definitely do check out what's being offered, and don't be scared to reach out :)
good luck, especially with the strict professor
hopefully they aren't as bad as they seem...