Everyone worries about their arms i reckon. My hubby gave me some tips which i used to use when i wanted to tone them up for our wedding. (I now don't bother coz i have a bub who weighs 8.5kgs & I recokn that's weight lifting enough....heheh)
Anyway, he suggested using 2 tins of food....cat food, soup, baked beans whatever and with one tin in each hand and your wrists facing upward do some bicep curls bringing the tins up towards your shoulders. Repeat this 10 times on each arm (increase repetitions as your arms get stronger). Another one is with a tin in each hand bring the tins up to your shoulders and push them up toward the roof. Do this 10 tens on each arm. Another one is (do this one arm at a time) relax your arm so it's hanging by your thigh then extend it outward -sideways (hope this makes sense) Do this 10 times on each arm. Lastly leaning forward with one knee bent and one hand resting on that knee, with the tin in the other hand extend your backwards and up. Repeat this 10 times on each arm.
For a separate exercise stand facing backward against a benchtop with your hands resting on the edge of the bench, feet about 1 - 1.5 feet away from the bench. Bend your knees and go downward, do this 10-15 times, increasing as it eventually becomes easier. This is a great exercise for toning that baggy area on the upper underarm (The 'tuckshop' arm bit).
Hope all these exercises make sense, they do work but it will take a few weeks to notice any results. These are also great if you don't go to the gym or don't have any hand weights.
Good luck, and have fun.