First, I don’t think you have to worry about extra muscle making you sick. It should have the opposite effect. Second, it’s a personal thing of course, but I think more muscle mass on anybody is aesthetically pleasing.
The most effective way to increase muscle mass is a good weight lifting program, proper diet for your goals, and proper insulin dosage to maintain your BG in normal range and supply the insulin necessary for muscle growth. The trick, of course, is balancing all these variables to reach your goals and maintain your diabetes control.
If you’ve never lifted before, start slow, with basic lifts done properly. How much weight, how many reps, and number sets you need to do depends on your goals and your own personal physiology. The trick, of course, is finding the right combination of lifts, weight, reps, and sets to reach your goals.
If this all sounds vague, it’s because your questions and goals are very general. For more specific answers, you’d need more specfic questions.
For starters, look around this forum for links and ideas for specific training goals. There is a lot here to get you started.