Is there any treatment for early stage capsular contracture without surgery? Any medicine that can help the burning sensation?

Early on, surgeons try to use leukotriene inhibitors (such as singulair for example) to stop the capsular contracture.  It may not be very effective and you may end up requiring surgery.

In the early stages of capsular contracture there are some medications that may be beneficial. Speak with your surgeon about their recommendations for treatment of early contractures. If conservative treatment doesn't fix the contracture, than surgery will be needed to remove the scar tissue and place a new implant. 

Capsular contracture around a breast implant may have multiple causes, including infection, bleeding and inflammation. It is the development of scar tissue around the implant which can compress and harden the tissue around the breast. It can be associated with pain. Typically, an early capsular contracture is related to blood around the implant, which sets up an inflammatory response. Anti-inflammatories may be helpful, Singular has been shown to help with early capsular contracture, as well as external ultra-sound. Typically, over time the degree of contracture will declare itself and may need to be addressed surgically with a capsulectomy and breast implant exchange. 

You should discuss this with your surgeon, there are medications and physical treatments that can help, but you should not take online advice for those.  You should be examined by your surgeon and determine which treatment is best for you.

There exists evidence in the literature for the use of leukotriene inhibitors in the treatment of capsular contracture. These drugs are typically employed for the treatment of asthma and use in the setting of a capsule is off label. Typically, in early contractors a 3 month trial has been shown to have some effect on softening. However, an established and organized contracture which has already caused upward displacement of the implant is unlikely to show any improvement.As always, discuss with your board certified plastic surgeon.