Does she like me if she always has an excuse ready when I suggest plans

If she wanted to hang out, she would make it happen. She would move the sister thing, reschedule, suggest an alternative, or at least say 'I'm swamped this month but let's lock something in for later.' Instead she's giving you an excuse and a non-specific promise like 'soon' or 'definitely.'

Excuses are easy. They let her avoid the conversation where she'd have to say she's not interested. She probably likes the attention or the idea of you, but not enough to actually go out with you. That gap between the idea and the action is the thing that matters. A person who's into you finds the time. That's not a rule. That's just how people work.

A good reply puts the ball back in her court in a way that requires her to follow through. Don't offer a new date. Instead, acknowledge what she said and ask her to come back when she actually has availability. Something like 'Got it, just let me know when you're free and we can make it happen.'

Now she has to text you first. She has to be the one who brings it up and commits to a specific time. If a week passes and you don't hear from her, you have your answer. If she does text back with a real plan, great, she was telling the truth. But most of the time, she won't text. The lack of follow-up is the data point.

Send one reply after the excuse. Just one. Something that puts it on her to reach out next. Then wait five to seven days. Don't text her about anything else in that time. No memes, no 'how's your day' messages. If she was interested, she would use that week to text you with actual plans.

If you don't hear from her by day seven, move on. Not in an angry way. Just accept that this isn't happening and stop looking at her messages. If she texts you three weeks later, you can reply, but don't go back to asking her out. At that point she's shown you where you stand. Respond if she initiates, but don't initiate again.