Wear clothes to go swimming! (It sounds silly, but hear me out!) There is no need to miss out but you should feel comfortable, too... Get a cotton T-shirt, or cotton jersey shirt, and (since you say you won't wear shorts) get a light weight pair of cotton pants (Like pj type) and wear that!
Then you can go swimming - still be covered AND it will create what swimmers call 'drag'. That means it will cause resistance in the water and it will be GREAT for a little exercise. (If anyone questions why you are wearing clothes - you can tell them it is part of your exercise routine and explain the drag it creates!)
Please don't miss out on the swimming with your family - they love you no matter what! I love swimming, and I can not imagine my life without it - even if I weighed 800 pounds I would still be in that water.
My friends and I skinny dip at night on labor day weekend every year! Just think if it! Me and my 200+ lbs flopping around in the water naked!! (at least you don't have to worry about skinny dipping! lol!)
