Brief Answer:
Postural hypotension

Detailed Answer:
Hi,
I am Dr. Prakash HM and I would like to answer your query.
Looking at the two symptoms, one of dizziness and other swollen left hand, both appear to be different.

Dizziness:
Dizziness in the elderly is commonly seen due to baro-receptors reduced function (these are receptors which stabilize blood flow by constricting blood vessels). This condition is called as orthostatic or postural hypotension.

When she gets from sitting to standing, or sleeping to standing, she will feel dizzy, as it takes more time than normal for blood vessels to stabilize and take the blood to brain. Because the brain feels it does not have oxygen, it makes the person lie down, and this feels dizzy.
People are known to fall suddenly and this could be dangerous - risk of fractures, head injury etc.
She needs to move slowly from each position, so that baro-receptors can adjust. If she is not hypertensive or on treatment for hypertension, salt rich diet can be used. If she is on any medications particularly related to depression, head ache - you need to look at its side effects, as some could cause dizziness.

Swollen left hand:

The swollen left hand appears to be due to local cause - arthritis of the wrist or fracture. If there is even a history of mild injury, it would be fracture. If present since long, it looks more arthritis related. You need to get an X-ray for confirmation and an orthopedic surgeon opinion.
For swelling, you can use ice packs.
For pain, local NSAIDs spray, capsacin creams can be used.
She might be already on painkillers orally, so I don't want to add any more prescription.

Any further queries, happy to help again.
Dr. Prakash HM

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