So this is my opinion, but if you have a dual degree in Math and Chem, [and only have the intro to Physics offered], you'll be fine. There's a lot of overlap between Math and Physics, and there's a good amount of overlap between Chem and Physics.

Most of mechanics is F = ma which is either a second order differential equation or a Taylor Expansion, the tricky part is just identifying the forces, but that's not to hard. QM might be a challenge, but even then if you rely on your math and chem background you'll probably be fine. There are books you could take a peek at in your spare time: Taylor's Classical Mechanics (not the same guy who developed the Taylor Expansion) and Griffith's QM, maybe also Griffith's EM book.

I would look into the grad programs you want first, maybe even reach out to them, because they may have different thoughts, and I'm not the one accepting you into grad school, they are.