First things first, stop using Antibiotics they will kill all the healthy gut flora inside your body. Be careful what the dermatologist prescribes for you. You have to tackle this by trial and error and be careful not to use anything too damaging or completely off limits and this includes Antibiotics , cortisone creams etc..
I recommend you try coconut oil because it will reduce the redness caused by the inflammation. It will help moisturize the skin so you get a 2 for 1 benefit from it. Try soaking in the bathtub with dead Sea Salt . It will help calm your skin down.
I would not advise you use baking soda. The burning sensation is caused by the baking soda. Its harsh on the skin and a great around the house cleaner but its way too harsh to put on the skin.
Look into eating a healthier diet with lots of omega 3/6, vegetables rich in minerals, probiotics and water. Avoid processed foods, alcohol and oral Antibiotics .