Im gonna sound like a broken record but ice and anti-inflammatories SLOW healing they do not help it!
Just think this through and ask yourself how does the body heal itself, just at a basic level? It needs to get raw material to the site of injury and get damaged tissue away. How is this material moved? By and large it moved through the blood stream. What happens when you apply ice to the body? The arteries become restricted and blood flow is reduced!!! So if the goal it to heal something then why on earth do people insist on doing everything they can to SLOW down the process? And that doesnt even take into account the necessary players drawn to the sight by chemical messengers. SSpoend some time googling the "healing cascade".
The medical community will argue that excessive (and that the keyword) inflammation can actually hinder circulation and I will give them that. However that generally only applies to acute injuries with massive noticeable swelling, for example a twisted ankle that blows up the size of a softball and even then should be used sparingly and only right at the time of injury.
For chronic overuse injuries ice you use ice and anti-inflammatories to help with pain management but that comes at a great cost and thats the cost of healing. Usually this devolves into a long term downward spiral which can often end in permanent damage.
I first recommend eliminating mechanical stresses, outside lifting and the like, that may be subjecting the area to unneeded additional stress, ie Adhesions and the like. Deep tissue massage, ART, band flossing etc.
Next are you getting the raw materials in ample amounts to facilitate repair for the amount of damage that is beiing done by repetitive movements? The answer here is generally no, especially for athletes. Most people dont even understand the process by which healing takes place or the required nutrients to facilitate repairs and the government and the medical system are clueless as well since the nutrients would trump their ability to peddle meds and make a profit.