Thanks for using the forum. I am happy to address your questions, and my answer will be based on the information you provided here. Please make sure you recognize that this forum is for educational purposes only, and it does not substitute for a formal office visit with your doctor.
Without the ability to examine you and obtain a history, I can not tell you what the exact cause of your symptoms is. However I will try to provide you with some useful information.
It sounds like you have some burning throughout the body, but with some associated viral symptoms. During and briefly after a presumed viral illness, headaches and some aches and even burning (due to neuritis or a neuropathy) can occur. Post-viral symptoms could last a few days. One neurologic cause of burning is neuropathy, a nerve problem due to various causes. There are certain post-infectious conditions that can lead to neuropathy such as Guillain-Barre syndrome, but these are often accompanied by weakness in the extremities. Some viral illness can affect the brain and/or spine, leading to demyelination (not as in multiple sclerosis, but a similar process). If by dizziness you mean light-headedness, with viral illness is not uncommon, and it is important you make sure you are not dehydrated.
Postinfectious symptoms often resolve with a few days. however if your symptoms persist, or new ones develop and/or you continue to be concerned, evaluation by your primary doctor is recommended, with referral to a neurologist as indicated. If your burning is deemed secondary to a neurologic cause, there are treatments for neuropathic pain (pain coming from nerves) that can be very effective.
Thank you for this opportunity to answer your questions, I hope you find the information I have provided useful, good luck.
I'm not an MD, but a fellow burning pain sufferer. I hope you get some answers and feel better soon. I have Lyme disease, apparently, which is probably causing my burning pains. At first, they diagnosed me with fibromyalgia, then they felt it may be a "post-viral" syndrome. I didn't remember any flu-like symptoms, but it looks like you have had viral like symptoms. Perhaps it is something like that?