Some sprains are very severe -- many years ago I turned my ankle and sprained the 2 outside ligaments. My foot and ankle swelled up like a Christmas ham, and I was off my feet for 6 weeks. The ankle was painful for the following year.
Signs of a severe strain are continued swelling, discoloration of the ankle and foot, and pain to the touch in the areas of the ankle ligaments.
Sometimes a bad sprain includes a micro-fracture of the medial or lateral malleolus -- the ankle bone. Whether fractured or simply sprained, the symptoms are the same.
Turning the ankle rarely requires treatment of this fracture. In general, RICE and physical therapy when inflammation is reduced are the preferred treatments. Use of NSAIDs can help, and sometimes a mild opioid pain reliever is prescribed. (Always take NSAIDs with food and be mindful of daily maximum doses).
With breaks, pinning the effective bone can greatly assist healing, however, most sprains are treated effectively with RICE.
These days orthopaedics is an excellent source of splints and other prosthetics to protect the injured joint and musculature, and help you walk in the injured foot. These devices can be pricey and require a visit to your local bone doctor, however, for those with insurance, they can be well worthwhile in speeding up healing and preventing reinjury. The natural muscular action of walking helps reabsorb interstitial fluids which reduces swelling, and promotes healing of connective tissue.
However, because fractures need a little time to heal, I've used crutches for severe sprains. Some doctors believe that the use of crutches delay healing. Personally, with a bad sprain, I believe they're necessary for a few weeks. Crutches are available from most pharmacies at a price around $50.
Find a good position for elevating that foot, and keep a ready supply of ice. It sounds as if you're going to need more weeks of recovery before inflammation is reduced.
Once swelling has stopped, warm soaks can help reabsorb some interstitial fluids.
Protect the ankle and use compression with an Ace bandage. Try to make small movements of the foot (but never force yourself into pain.) This will also help reduce some of the inflammation.
Get yourself some good books, or a collection of favorite films. Sounds like you're going to be laid up for a while.
Best wishes for rapid healing.
Go to a doctor. Do not pass go. Do not collect two hundred dollars.
You need as film at the least and an MRI, preferably.
The reason is this. If there is a fracture there is a window of opportunity to secure the bones, and if lost, they will not knit.
This is probably a sprain. but not necessarily.
Differential diagnosis is not that easy.
You need to be seen urgently and get an image done of the foot.
As you have had the problem for over 2 weeks, I do not know how your ER works and whether you would need a referral from your doctor for an xray at least.
In the meantime, keep off the foot as much as you can, bandage it lightly for support (you may find info how to do a support bandage on the web) and keep the leg elevated.
Most mild bone breaks take around 6 weeks to heal.