I am not on any medications, tremors in head hands and legs for over a month. Constant dizziness and trouble speaking now, also hair loss. Any ideas?

Doctor or ER. You need a full work up with blood work, physical exam and possibly several types of imaging of your brain, its supplying blood vessels and heart. A lot of possibilities and many of them could be quite serious. If you really can't speak or are slurring words and dizzy get to the er.
Get checked ASAP! Could be hyperthyroidism, vitamin deficiency, toxin or hormone problem, among other things. Could also be just the side-effects of something worse. The trouble speaking is quite concerning and needs immediate workup. Wait too long and your treatment window can close.
Unusual. One possible explanation for your combination of symptoms would be neurosyphilis. Please see a doctor immediately and get tested.

Related Questions

Hair loss, tremors in arms, hands, legs and feet, loss of balance and strength, numbness in legs and feet all after a lumbar puncture, why?

Unrelated. Why did you need an LP. Problems from spinals affect areas below the spinal it lower torso, legs, urination etc, It would not affect hands or make you shake, It may be part of why they wanted to examine your cerebro spinal fluid. Discuss with your MD or neurologist.