It is unfortunate to hear that you have been putting up with this for so long. It is obviously very hard to try to make a diagnosis without being able to actually examine you, but can I ask a few questions to get a bit more detailed information from you?
a.) When you say 'hip' where exactly do you mean? In you groin, on the outside of the hip, more to the back near the buttock?
b.) When you were thirteen and your hip clicked for the first time, how severe was the pain? How long did it take to settle down? Did you have any weakness associated with the pain?
c.) Is the pain with you all the time? Are there any activities that make it worse apart from prolonged standing/sitting? Which part of the pelvis would the pain shoot across? When you say you get aching down the legs, exactly where does the pain travel? Is it a generalised ache all over, or more to the back of the legs/side/front? Do you get any tingling/numbness in the legs at all?
d.) Did your physiotherapist look at your spine at all? Did they doublecheck that there isn't a lumbar spine involvement in your pain?
e.) Which exercises (basic strengthening) were you give to do? Which flared you up the most? Do you still do them?
As far as pilates is concerned, it is a great idea to help strengthen up your core, particularly if you have hypermobile joints -- as your limbs require a nice stable core if your muscles want to work effectively. As a physiotherapist, and as someone who also has gross generalised hypermobility, I would advocate it strongly -- regardless of your hip problem. If your physiotherapist is trained in clinical pilates, then they should be able to set you up with a simple mat-based pilates programme that you can complete at home. All you really need is a yoga mat and yourself.