Parkinson's disease most commonly presents at its onset with a resting tremor in one hand. The diagnosis is usually made by a set of findings that include resting tremor, a history of slowing down and rigidity. It becomes more and more common beyond the age of 50 but rarely can occur at a much earlier age (around the age of 30), which implies a hereditary form. The only symptom you describe does potentially appear consistent with a diagnosis of Essential Tremor; this type of tremor runs much more commonly in families than does Parkinson's Disease. I presume the Neurologist who saw you took the time to get a detailed account of your symptoms before doing a full neurological examination, prior to making the diagnosis.
If the diagnosis of Essential Tremor is valid, then you are on one of the first line medications used for it. The fact that your tremor has not improved may relate to the fact that you are not on an optimal dose of medication, or may be because the medication is not the right one for you
(there are other medications available for the treatment of Essential Tremor). The dose of 40 mg of propanolol (Inderal) twice a day is still a low one and there is room for you to go up on it. It may well be that a higher dose will provide relief from your symptom.
You should see your Neurologist for regular follow-ups as it allows them to keep a record of your symptom and to assess the effectiveness of any medication they have prescribed. As the beta-blocker is also being used to control your blood pressure, it is important for your Neurologist and Cardiologist to co-ordinate your care. I would as a first step go back to the Neurologist and let them re-assess you.