Should I get my brakes checked?

My parents own a 2009 Ford Focus that I've been starting to use most of the time now to drive to school. Last week, I just got an oil change done and had loose links replaced for the front sway bar. Tire rotations and fluid top offs were included as well. I realized a few days later that the brakes were stuttery or jumpy (I didn't feel it in the brakes, but when I used the brakes more gently, I could feel the car kind of pulse to a stop instead of smoothly glide to a stop). A few times, a warning flashed quickly that the brake fluid was low for a split second and then turned off. My dad topped off the brake fluid and said not to worry because the brakes were replaced last year. I don't know if I trust what he says because he also takes his other cars for oil changes when they're way overdue and says they're fine. If I continue to have these problems, my dad will probably say I'm overreacting and he won't want me to take the car back in. What should I do?
Added (1). The car's steering wheel also vibrates at a stop

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