Also, Chemistry does deal with protons, one of the first things I was taught was that you can identify an element based on how many protons are in it.
Yes, protons ARE involved in a discussion of chemistry, but it's more to do with the electrons than the nucleus, when it comes to chemical reactions. I can't think of any chemistry that would require understanding of protons on the fundamental level in which particle physics handles them. It would be akin to saying that since understanding of electrons and charge flow is essential to electrical engineering, that you need a strong background in EE to understand Maxwell's equations or quantum electrodynamics.
Here's the line you'll want to draw: chemistry deals with atoms and molecules, in an attempt to understand how they react with other atoms and molecules. The fact that there are protons in these atoms and molecules is of little importance. The electrons are of importance insomuch as it's important to understand how these electrons are configured in an atom in order to understand why atoms and molecules can bond with one another in chemical reactions.
Particle physics asks more fundamental and existential questions about electrons and protons: Where do they come from? What gives them mass? Do they decay? What decay processes produce electrons and protons? Are there antimatter or supersymmetric partners to the electron and proton? How can we make electrons and protons interact in such a way as to create other particles we want to know more about? etc, etc. The science behind these questions is VERY different than the science behind chemistry. Being an expert in particle physics would not really help you be a good chemist and vice-versa.