The lymphoedema swelling may be a constant reminder to you that you have had treatment for cancer - something you perhaps had hoped to forget as much as possible. If the swelling is severe, you may feel embarrassed and self-conscious about it.
Try not to shut yourself away. Almost certainly, the swelling is more noticeable to you than it is to others. If you are nervous about going out in public at first, ask someone you know to come with you. You will probably find that no one makes an issue of your lymphoedema.
As your lymphoedema becomes more under control, and as you get more used to it, you will almost certainly find that your feelings of embarrassment lessen. You will probably realise that true friends care for you because of the person you are, not for your appearance, and this will increase your self-confidence and make you feel more in control of your life.
If you have very obvious swelling, some people will inevitably be curious, especially children. Many people find it helpful to rehearse what they will say in such situations. Your lymphoedema therapist or nurse may be able to help you plan and practise your responses. Or you may prefer to talk about it with other people who have lymphoedema.
You could decide how much you want to say about your condition, whether to refer to your cancer or treatment. Once you have a prepared response, you are less likely to be thrown by any remark or question directed to you. You may even find yourself actively helping others to overcome any awkwardness they may feel.