What can you do to help yourself? Well...inflammation that is out of control causes scar tissue to build, so post hip arthroscopy take the anti inflammatories prescribed by your surgeon. Do not push yourself too hard in your day to day activities and rehab in the weeks after your hip arthroscopy surgery, as recurrent micro trauma of the site may encourage scar tissue to build. It is said scar tissue can start building as early as 2 hours post surgery.
You need to insure you keep a good range of motion so that the scar tissue is not allowed to limit this. Do listen to your physio regarding types of stretches and exercises that can can help you with regaining your ROM, as well as your strength.
Icing the site is a cheap and easy option which can be done several times a day. Ice helps combat inflammation and has no systemic downside.
There are also some supplements that can help and can be taken in tablet form, if you feel unable to incorporate them into your diet.. you will find turmeric, omega 3's and bromelain (from pineapple) can help you fight inflammation. Do check first though with your healthcare provider that there are no problems with you taking such supplements.
I am posting a link to a site here which advises on anti inflammatory foods to help relieve the swelling. Never under estimate the power of the fuel we fill our bodies with, it is an unfortunate truth that sugars and alcohol are true irritants and pro inflammatory to our bodies. I'm not so unrealistic as to say you can't have a bit of the bad stuff, just try in rehab to tip your diet more towards the anti inflammatory foods, even if it means subtle changes like switching cola for a pineapple juice and regular potatoes for sweet potatoes. There is more you do to help yourself than you might think.
It also explains the inflammation to scar tissue process.