Q:

How deep can my knowledge of particle physics go without the maths?

By no means do I have the mathematical background to understand most of the math used in elementary particle physics. 
My current knowledge is of all the elementary particles and how they interact and build upon each other to build the macroscopic world. 
Will I be able to continue forward and understand more in particle physics or should I stop now and start learning probability theory and whatever else I might need?
Is there a place where I can start to learn the maths? Is there a place where I can learn all the maths but on a novice level? 
The coolest thing I have seen/understood is how the electromagnetic force works: Photons bounce back and fourth between particles in atoms creating the force field. So the thing that keeps my hand from going through the keys as I type is the electromagnetic force, specifically photons (please correct me if I am wrong about any of this).

A:

I don't think it is possible to learn physics without math. Mathematics is the language of physics and you can't learn a subject without learning its langauage. (This is just my opinion though). 
To start with particle physics, I think you should first learn quantum mechanics and special relativity. For quantum mechanics, grab a copy of Griffith or any other similar book. Knowledge of single variable calculus and differntial equation is needed though.For vector calculus, you can look into the first few chapters of Feynmann lectures vol 2. Along with these, you must also learn abstract Linear algebra (theory of vector spaces) , very basic group theory (definition of group and group actions) and multivariable calculus.
Once you are done with qm and special relativity, you will be ready for Quantum Field Theory.A nice book for QFT is Quantum Field Theory in nutshell by A. Zee.
Also,, now you should learn about theory of group representations and lie groups. A good introductory book for this topic is Group and Symmetries by  Yvette Kosmann-Schwarzbach. The last chapter deals with particle physics.
Note that this route won't make an expert on the topic but you will gain a good understanding of it.

