It might be helpful to get your child a fun and colorful swimsuit that fits well so she feels less self conscious, as this may be more about how she feels about her appearance than about her ability to swim. Take her to a quality swimsuit store and let her choose one she really likes; have the assistant help make the choice if you need. Also, spend some time talking to her about her fears and seek to reassure her. Explain too that the buoyancy of water helps all humans float and that swimming is an easy form of exercise to keep fit without sweating or feeling the challenges that can come with land sports like running and cycling. Last but not least, offer to go swimming with her and help her to learn how to swim properly; that way she'll be happy that you're truly invested in her efforts to learn swimming.