Was I wrong in responding this way to my boss when she asked me if I could work?

She just said “Ok” in response.

Sounds like you handled this correctly. Never give a reason when you are declining a work request.

Okay… that’s good. Was worried because this is my first job and I don’t know how to respond to this kind of stuff, without being rude, and also because it was over text and I wasn’t sure if it was an actual question or not. (without a ”?” as well)
Why should you never give a reason?

The most commonly used and accepted response to last-minute requests (and a “same-day” request for spot overtime is roughly equivalent to last-minute) is “I’m sorry, but I’ve already got plans.”

That works whether your plans include a date, elective surgery, to do some shopping because you’re out of food… or just to go home and take a nap because you feel like it. And as @thisismyusername noted, you don’t volunteer that reason.

Now, if she asks “Can you work late next Monday?” then you might need to have some more concrete refusal, and that might include “a reason” (depending on how you feel about the job, the boss, the firm, etc.), and “because I don’t feel like it” might be career-limiting in that firm.

Giving a reason should generally (i.e. unless your contract legally specifies otherwise for good reasons) both not be their business as your employer/manager (on your own time, you should not be obliged to reveal what you are doing (“Sorry, I’m in Vegas with yo momma.”), and also could be something they could judge you with, possibly unfairly.

I used to just say, “I was supposed to babysit for my sister, but I will call her and ask her if she can find someone else”. 99% of the time they would say they can find someone else.

Yeah, generally when you tell someone – at least on the last-minute thing – “I’ve got plans” (whether you do or not; that’s entirely up to you) that’s a valid excuse for not doing whatever you’re being invited to at this late date. If someone asks you directly, “What are your plans?” then you should just look at them cross-eyed as if they turned around and farted in your face. That is, for them to ask “What are your plans?” when you’ve made that excuse is that rude of them.

Now, they might ask “around” that: Are they plans you can’t break? How about this other thing that I have planned, doesn’t that sound more exciting? etc. That’s fair. But to ask you point blank about YOUR plans that don’t include THEM – that’s rude, and while you don’t have to tell them that (as if they don’t already know) that’s something they should know.

Again, when they ask ahead of time – and how much time ahead is up to you and the way you normally make plans, or the particular day that they’re asking about – then “I’ve got plans” for a random date in the future is rude on your part. (And sometimes, like when you’re trying to avoid a date request from a particularly unwanted yet persistent suitor, it’s just what you need to get the message across.) It’s expected that many people would have plans on special days: self or family birthday, national holidays, anniversaries, etc., but for “a week from next Tuesday” for you to respond automatically with, “Can’t, got plans” is a brush-off, and will be read that way.

Your question has been answered quite well already, but I understand your fear of doing something wrong with your first job. I know at this point the more support you can get for how you handled things, the less you feel that knot in your gut.
You did just fine.
Here is the scene…
Jobs which involve lots of teens and/or single parents (sick kids) on the schedule tend to have employees calling in at the last hour, or just not showing up.
As a result, they are going through their list of people who might be able to fill in. Doing this is a nightmare, and they have to just hope they can find someone with basically no life. They actually PREFER a quick yes or no, so they can fix the problem quick as possible.
What you do with your time is none of their business, and mostly they couldn’t care less anyway.
If you want to help out, but you really do have previous plans, you might say, I have plans, but, if you try everyone else and don’t get someone call me back, K?
The better you can help, the more they come to appreciate you. The quicker they move on when you can’t help is also appreciated.
It is not like school. Your boss doesn’t want a story. They just want the shift to go smoothly.
Now, if you are scheduled, and you want out of it, some story might be expected.
Since your boss asked in a text, they probably sent one text on a list type send, to hit everyone at once, and waited for people to respond. Gawd, sometimes technology is so great. Imagine, in my teen days, to reach all employees like that required separate calls (no texts back then), punching seven buttons, waiting through rings for someone to answer, usually a sibling or mom, waiting for employee to get to the phone…
Well, a list text must be a sweet change for managers!
You see how they just want a quick, no frills answer?
Again, you did just fine.