As so many others have said, unfortunately, we cannot spot reduce fat in our troublesome areas. First, take a hard honest look at your diet and see if you can reduce your sugar and processed food intake. Recent science has shown that hidden sugars are everywhere in our food supply (even natural foods) and these excess sugars are stored as fat in the body. Losing body fat is about 85% of what you eat and 15% exercise.
Second, like so many others have said, incorporate a combination of cardio and strength training into your workout routine. Cardio helps burn off the fat and tone up your cardiovascular system, but muscle will burn even more fat. Strength training is also great for your bones. Using your own body weight as resistance is a great place to start; pushups, plank position exercises, tricep dips are all great places to start for working on your arms. Pushups and plank exercises are great because they also work your shoulders, chest and core.
Once you're feeling comfortable using your own body weight, move to light hand weights for bicep curls, hammer curls, shoulder press, tricep extensions and tricep kickbacks. Make sure your movements are slow and controlled until you are comfortable using them, to avoid injury. Start out with 3 sets of 8-12 repetitions. Know your limitations and never compromise your form. Hope this helps and good luck to you. With time and due diligence, you'll get there : )