Sounds like you do have time, you're just not using it wisely and don't have the motivation to clean. You say you work full time, but that usually means 5 days of work so there's two days a week you don't, and Univ 4-5 days for 4 hr, sounds like there is time for you to clean. Even on a day you have both, that leaves 12 hrs, 8 for sleeping then 4 others, say even if 3 of those are for commuting and doing things like eating and showering, that leaves 1, even if you take 10-15 mins and start to clean, eventually things will be cleaned up (maybe a week). Then once things are cleaned up- don't let it get messy again. Put stuff up immediately after use, do the dishes right after using, stay on top of things don't just put off. If you say "but I'm never home!" If was true home wouldn't be messy.

You do not have to clean the whole place at once, break chores down and do 1-2 a day. And get on a routine.