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 definitively what your brain is from however I will try to provide you with some useful information.
The left side of the brain is related to the right side of the body. In order for a lesion in the brain to be causing both right arm and right leg, it would have to be on the left side of the brain. Without viewing your MRI, I can not tell you whether or not the lesions you have are causing your symptoms (and our role on this website does not include reviewing MRIs). However, the right parietal lobe lesion would not be the cause. The left white matter lesion could potentially be the cause depending on exactly where it is.
Dysfunction in the brain can lead to pain on the opposite side of the body by either affecting sensory areas (some of which include the thalamus and a part of the parietal lobe) or by causing spasticity. It is important to understand if your pain is due to stiffness (the medical term for which is spasticity) or not. Spasticity is often caused by brain abnormalities (or spinal cord which it sounds like in your case does not have any abnormalities on MRI). There are specific treatments for spasticity if it is present. Spasticity (stiffness) is diagnosed based on physical examination (a feeling of stiffness does not always imply spasticity, spasticity is a physical exam finding made by a physician).
It is important to keep in mind that the lesions on your MRI may be nonspecific, if they are small and have a specific appearance, they may related to your migraines but may not be a direct cause of your symptoms. There are multiple causes for so called white matter lesions in the brain. Most often, these are due to what is called "chronic small vessel disease", literally meaning diseased small vessels that supply blood flow to the brain. This is not an uncommon process in the brain and increases with age. Other causes of white matter lesions in the brain can be migraine. People with migraine often have white matter lesions on their MRI that are of unclear cause or significance.
Other causes of white matter lesions on MRI can usually be distinguished based on history and symptoms, such as symptoms of neurologic deficit (for example arm weakness or difficulty walking etc). These can also be distinguished based on the MRI appearance. These include, but are not limited to, multiple sclerosis, other demyelinating disease, cancer metastesis, infection, and inflammatory processes such as vasculitis. The diagnosis of MS is NEVER made based just on an MRI, several other factors such as your history and physical examination are taken into high consideration as well.
It is unlikely that the abnormalities seen on your EEG are related to your pain because a temporal lobe abnormality would not really cause pain on the other side of the body unless there was a large structural lesion there pressing on surrounding structures which it does not sound like is the case in you.
I encourage you to continue to follow up with your neurologist to better understand what your pain is from and how it can best be treated. Keep in mind that topamax is a great treatment for migraine but can actually cause numbness and tingling. However, the numbness and tingling caused by topamax is usually in both hands and feet in the finger tips and toes rather than on one single side of the body.
Thank you for using the forum I hope you find this information useful good luck.