Was this a good " sick day" excuse?

You started the end of March, we're one week into April. Good luck with that.

No excuse is a good excuse a couple of weeks into a new job. You were a fool to ask for a day off if you didn't 100% need one.

And of course she was right to ask 'what kind of emergency?'. Because people's notion of an emergency that calls for a day off varies - some people will come in and do a day's work with two broken arms, and others think having had a row with their BF is an emotional emergency that justifies them in staying home. There are people who have been at my workplace for a long time, that if they phoned saying 'family emergency, can't come in tomorrow', I wouldn't think of asking what it's all about and does it really need them to take the day off, because I know them and I know they wouldn't ask if they didn't need to. All I'd ask is, 'do you think you will be in the day after that, or do I need to make contingency plans in case you can't?' But someone who's only a couple of weeks into the job and calls in with a vague statement like that - d*mn right I would want them to be a bit more explicit about what family emergency and why you were needed more there than in your job.

No, it was a silly lie, and made worse by the fishy way you tried to avoid telling it at all. (It could yet catch you out, if a few weeks on she asks how your sister is and you've forgotten what lie you told.) You had better make up your mind not to throw any sickies, even if you really feel ill, for another three months at least. You have now marked yourself as 'potentially unreliable, possibly a liar', and you'll need to stay squeaky clean for a long time to wipe out that early impression.

You still have the option of going to work tomorrow. I think that would be your best solution to your conundrum.

At my job you cannot call out during the first 90 days without being fired.

It was a lame excuse.

No - that was a lame excuse. And you are also a liar, which you shouldn't be glad about.

No, start looking for another job.

you shouldnt lie just to take a day off, they really need you or they wouldnt have hired you, that would be a really good way to lose the job, just being honest

What does "broke her food" actually mean? Tell the truth but don't expect you'll have a job either.

Just say "I'm not feeling good"

The correct answer would have been, "as a matter of fact, I do mind telling you the details of my personal life, so F*CK OFF." It sounds a little harsh but the manager would respect your courage and you would probably have gotten a promotion.