You will need to add to your home gym...a bench with some weights and a bar will get you started. You need to work on the basic exercises in order to gain solid muscle all over your body. You arms will grow when you make your whole body grow. The exercises that need to be your focus include...
Your diet needs to be as clean as possible most of the time with some cheats now and again when you need it. Proteins are your first priority...steak, eggs, fish, milk, chicken, turkey, etc. Next is carbs...oatmeal, brown rice, whole grain bread, pasta, potatoes, yams, fruits, and veggies.
Protein powders and protein bars can also be good adjuncts to your diet.