Originally Answered: How to burn fat in my arms fast?
Swimming is a good idea, and working with weights will help to tone up the muscles in your arms; that will mean they burn more fat while they are not training. Push-ups will also strengthen the muscles, but without making them any smaller.
The best way to change rthe shape of your arms is to do plenty of exercises that do NOT involve resistance. The 'classic' example (from boxing gyms) is punching a 'speed-bag', which is the small round punchbag that bounces off a board every time you hit it.
You can imitate this exercise by tying a small towel into a loop, or using a fleece neck-muff. Put both hands through the loop in opposite directions, so that you can hold the loop tight by pulling one hand towards you and pushing the other one away. Keeping the loop tight, start to rotate your hands around each other. Making this movement faster without letting the loop go slack will be very tiring, but by doing it as often as you can you will train a lot of muscles in your arms and shoulders.
This will improve the local circulation of blood as well as making the muscles stronger and more toned, so your body will release more fat from storage nearby as well as using more fat for fuel.
Make sure that your neck, shoulders, and breathing aren't tensing up when you do the exercise. That means you will probably need to limit yourself to very short bursts at the beginning, and aim for longer periods of training as you become more able to stay relaxed while performing the work.
4 weeks isn't long to make a visible difference in the shape of your upper arms, but by working (not hard, but as often as possible) regularly you will be able to start seeing a difference, and you will certainly feel one.