Hi there -
I hope by now you've had a complete neurological survey. From the signs and symptoms you describe, something is definitely wrong. It may or may not be serious, but it is certainly going to interfere with normal functioning.
The room spinning is due to vertigo. Whether or not it is benign positionial vertigo or due to some central cause is important (and easy) to determine right in a doctor's office (or even the waiting room sometimes). If moving your head, looking up or down, or change of position triggers this, it is positional and so probably benign. However, you have other, associated neurological symptoms which are of more concern. The balance/weakness problem is very likely due to peripheral neuropathy of the legs (it may be present in other parts of your body too, but it is usually the legs that cause the most unexpected loss of balance). Peripheral neuropathy, along with vertigo, can make for a very terrible experience and creates a fall risk that must be born in mind at all times to avoid injury due to striking one's head during a fall (and you may not realize you're falling until you're more than halfway there, "there" being the floor or whatever's nearby). The symptoms of most concern, however, are the short term memory deficit and the localized head
pain with vision disturbance.
You'll need to have tests done to rule out MS, a growth inside the skull, and a number of less complex problems. MS often presents with these symptoms, so an MRI of the brain, as well as nerve conduction study, electromyelogram (EMG), and electronystagmogram should all be done, and done promptly. A complete neurological workup is completely warranted and should be done urgently, both to rule out the more serious (although usually manageable) problems, plus means to treat the immediate symptoms in order to reduce the chances of injury due to a fall.
I hope you will persue this aggressively and assertively. Please follow up with us here as needed. Best of luck to you.