You should just describe it to you your mechanic & have him/her take it out and do some hard braking. I can’t really tell if you’re describing a shimmy - that would feel like a vibration, felt in many places but including the brake pedal - or a swerve. The thing about a shimmy is that it normally won’t go away completely.
What you’re describing is either a) (swerve) a very dangerous condition involving any number of issues having to do either with brakes or suspension & steering (sticking brake caliper; bad flexible brake lines; bad struts; bad tie rods…); or b) (shimmy/vibration) a less dangerous but far from optimal problem with the brake rotors. A full brake job would be the best way to go. This problem can also come from worn suspension & steering parts though.
Either way its not good. Your brakes aren’t working right. Have it take care of. Its more important than the oil change.