Yes, P-chem is physical chemistry.
Once you've covered general chemistry the 'generic' path is organic, followed by physical chemistry with inorganic chemistry taught before, during or after p-chem depending on how it is taught. An analytical chemistry lab is taught somewhere in there too, at my school and my previous college it was taught around the same time as organic.
Now that you've done general chemistry, organic and have the necessary physics and math background, you should move onto physical chemistry, and if time allows, inorganic chemistry.
For physical chemistry, try and get a textbook like Levine or Atkins imo, they're pretty standard but fairly good. For inorganic, I like Miessler myself.
If you want a somewhat non-standard route for physical chemistry, get McQuarrie's physical chemistry book which teaches quantum first.
You could technically specialize now but the only thing you could specialize into is organic. Before thinking of speciliazing get a taste of all the fields - organic, inorganic, physical, biochemistry and analytical.