First off, major kudos to you for losing weight and wanting to do something to improve your health and appearance!!
For flabby arms, you should do a variety of exercises that will target the tricep. Pushups are great and don't require any additional equipment, but if you only do those you don't get all the different "heads" of the tricep. So, here are some examples...
Overhead tricep extensions: take a weight, hold it in either one or both hands, lift up and over your head keeping your elbows are pointing up to the ceiling and the weight is behind your head. And lift straight up, still keeping elbows pointed to the ceilings. If you don't have access to a hand weight, you can always use something like a jug of water.
http://www.youtube.com/watch?v=uPLWjJOJJ3I&feature=related
Tricep pushdowns where you are holding on to a rope thing that starts somewhere above your head, and push the end of that rope downward. Usually at the gym, I go to the machines where I can adjust the height of the cable, and set the weight at about 20-30 pounds. If you don't have access to a gym, try getting a hold of an elastic band like the ones they use for yoga. Or if you can't find those, then, get surgical tubing. Attach the elastic band to the top of the door frame so that the end of it hangs around your shoulder/chest level. Then you can grab a hold of that end with both hands, and slowly push it downwards.
http://www.youtube.com/watch?v=WaMY-...eature=related
Tricep kickbacks are where you find a bench, stick a knee on it and lean over, then holding a weight in your opposite hand in a bent up position near your chest, slowly extend your arm backwards.
http://www.youtube.com/watch?v=IuFEAtgBbiU
Tricep dips: position yourself in front of a low bench or chair, or any stable surface really, and put your hands on the bench and do reverse "push ups" keeping your body at a 90 degree seated position.
http://www.youtube.com/watch?v=ynVuH...eature=related
I would also work on your biceps though, to balance out the work on your triceps. Doing both tricep and bicep exercises will help in arm definition and create those nice "cuts" in your arm muscle.
As with most other toning exercises, the muscle definition really doesn't start showing through until you get rid of the fat layer over it by doing cardio. So, also keep up on your cardio, and do some of these exercises to create tone.
Swimming the front crawl, and paying particular attention to using the arms to pull you forward and less emphasis on your kicking legs was a great combination of cardio and arm definition for me. But I saw the most results from doing combined tricep and bicep exercises that targeted both muscle groups from a variety of ways. You will definitely see change over time if you do that. I know I did.

I used to hate my flabby arms, but I feel tons better about them now.
