I am sorry to hear of your recent diagnosis. I would definitely let your doctor know. Many people with MS have trouble regulating their body temperatures. They can also have all sorts of sensory things going on as well. You did not mention your age or gender. But you may want to consider your cycle or hormone level if you are a woman. This could be the symptoms of menopause. Even if you are quite young (as young as early to mid thirties) you can have hot flashes due to menopause. Autoimmune disorders can push menopause earlier.
Do the best you can to maintain a regular body temperature. If you are warm, drink cold liquids and get to cooler air. If you are cold, then go ahead and bundle up even if you are stripping it all off in a few minutes.
Be kind to yourself. It takes some time to adjust to all that has and is happening to your body. Welcome to the board and please feel free to post often; ask lots of questions or just vent. We are all very supportive here.