Good luck finding a good job bro. Getting laid off sucks.
Use it as a learning experience:
Still on probation and already coming in late - strike 1
Text instead of phone call to inform boss - strike 2
Smart ass email about planning sickness in future - strike 3
Telling HR you went to labor board and they were wrong and they owe you money - strike 4 and 5
Yer out!
Hiring a new guy is always risky. Probation is to find out how you will like them. What does a boss like? The invisible employee. He works, he goes home. The boss doesn't hear him ask for anything, doesn't hear his personal problems, doesn't have to cover for his absense, doesn't get messages or phone calls from him, doesn't hear complaints from other employees about him etc.
After this incident (even though it started out minor), they didn't want to take the risk of being stuck with a pain in the ass.
Better way to handle it, don't be late! But if you have to be, call boss, apologize 15 times, and thank her 15 times if she accepts your lateness this one time. Then tell her it won't happen again. Then tell her you are sorry for the short notice.
Then do a good job, day in and day out until they stop worrying about you and accept you. Then, occasional sickness or lateness becomes much less of a big deal.