I went through your complaints. If there is no infections and as you say that the pain is reduced with ice and heat therapy
- probably it may be muscle sprain
- which needs Elastocreepe bandage and complete rest along with the treatment you are already taking + foot elevation.
Better to add some pain killers and muscle relaxants. Strictly no practice of running for 30 to 45 days and after that slow starting as per the condition.
Meanwhile wear only chappals and no shoes