Myslef Dr. Shikha Goyal, I am an  Oro- facial pain specialist from Nair hospital, Mumbai, India. You can connect with us on my page with additional details of your problem. I will try to provide you with right diagnosis and guidance to go forward with the treatment.

Hello, The word TMJ Disorder suggests involving your temple region and the mandible i.e lower jaw. So pertaining to pain thats in the same region that you are depicting . So if thats your diagnosis after thorough clinical and radiological evaluation then you surely need to look into it for resolution of the problem. Pain can be a cause for TMJ related thing as well as tooth now there can be multiple things to manage your pain initially . For example keeping your joint warm with protective clothing ,applying a warm pack or using some drugs i.e muscle relaxant or a painkiller or combination of both which are usually prescribed.   My assumption on the radiographic picture of yours is there isn't any thing much to bother about teeth. Next thing is your swelling - an apparant swelling indicates an infection with increased temperature of the skin and redness in this case you should look for antibiotics and here you should avoid application of hot fermentation/compression  or hot food / beverages because this tends to flare the infection. This can be in your tooth ,neck(tonsils), parotid (salivary gland right in front of your ear) below which lies your tm-joint Comming to your mouth guards yes its one of the treatment options available effective in cases were patients compliance in good.