I'll see if i can answer that Rab, when working the chest the muscles you are using in your arms are the triceps (the back of the arm) and sometimes the delts, while biceps are mainly used when doing back exercises, so its better to do chest one day along with some tricep, and then do bicep along with back another day. to get your arms bigger i'd really recommend working out the triceps, as it gives your arm a nice shape if they're defined.
If you're finding its taking a along time, make sure you're changing your routine, never keep it the same, and always try to increase either the weight or the reps, doing the same routine week in week out on the same weight will not get results.
Even if you are just trying to shape up u still need lots of protein, that doesnt mean you need to have protein shakes or bars but ur diet needs to be high in it, and taking shakes does help to increase your intake (and is more effective), some amino acids such as l-glutamine also are very useful for quick recovery (and are not harmful). creatine can also be useful but for what u want i wouldn't recommend it.
hope that helped, feel free to ask any questions (I did A-level physical and sports studies and did a lot of studies on sports nutrition and other related things so I have a little bit of knowledge on this!

)