Recently my left hand has started shaking a good bit, but not the right. Left arm also feels a bit weak. 33/m. What could this be?

Needs an evaluation. The tremors could be due to ideopathic (doctors do not know) tremor for which some medicines will decrease the problem. Another cause is parkenson's which needs medical treatment. See a neurologist.
Go see your doctor. These are the kind of symptoms that you need to see a doctor for. Make an appointment and go in soon .