You don't mention if you are still seeing your therapist. You say you DID see one but not whether you are still going. Obviously if you aren't then you should go and see another one straight away. I say that because an eating disorder is a complicated thing that is only a physical manifestation of feelings you have on the inside. You have some sort of issue about either control or self esteem or whatever and you really need to explore your behaviour further in order to assess that.
I don't think the weight thing is really your issue here. I mean swimming is a calorie intense sport. You shouldn't have to worry at 5'6" if you're eating the normal calorie recommendation and swimming so much - it really shouldn't be an issue for you. Don't forget, btw, that muscle weighs significantly more than fat because it is more dense so if you build muscle by exercise and swimming and things you may actually be underweight compared to the "average" person your age and height who has less muscle.
So the weight thing really shouldn't be an issue for you and I'd be amazed if you really did find that eating say 1500 calories a day on that exercise was going to make you put on weight. I thin what you have to look at is your obsession with the weight and why you are so afraid of putting it on. It's not the weight itself that should be the issue for you - it's the process that's going on in your mind that is making you so obsessed with it. Why are you so scared of putting on weight? That's an issue that you can only really address with a professional therapist. If one doesn't work the don't be afraid to try another, btw. They all have different training and experience so if one doesn't work then you can always try another.
Have you considered seeing a dietician or better yet a sports dietician at the same time as your therapist. The reason I ask is because if you did that then you could ask them to teach you about diet and about food types and calories and digestion and by learning so much more about it you might find that you become more comfortable with it instead of fearing it because you don't know what's going on with your own body. If you had a dietician then you could be reassured that your weight was under control and that someone who knows about food was there watching and helping you out of you did encounter any problems as you up your intake. I juist thought that might add to some reassurance for you if you are going to be trying to increase you calorie intake.
Either way make sure you seek ro stay in professional therapy and never be afraid to ask if the therapy is working for you or whether you maybe need to try a different person. It's you that's important so make sure you get the best help you can. And remember to focus not on the weight but on whatever mental process is causing this fear - you are looking in the wrong place - at the symptom and not the cause.
Good luck.