Is there redness and pain?
Any color change to rest of hand/arm?
Any history of injury or recent injections?
It is unusual to have swelling of the artery, it is more common to get inflammation of the veins and as I cannot examine the area then I think you should get checked out today.
The lack of color change and pain means this is less likely to be cellulitis (a bacterial Infection of the skin) however any swelling affecting a blood vessel should be investigated.
Other swellings that can occur would be ganglion, but these do not typically pulsate.
Are you able to post a photo of the area?
Any tenderness when you touch it?
When you say it is pulsating, is this in time whith your wrist pulse?
Can you be specific as to the location? Is this on the wrist/on the chunky muscle at the base of the thumb or elsewhere?
Any overall fever?
Any warmth to touch of the area?
Why do you mention dehydration? What have you been doing today?
Thank you for the extra information. Obviously I cannot be definitive as I have not examined the hand however you do not mention any specific warning signs that would warrant a trip to A&E.
If you develop any change to temperature in hand (either hot or cold), or any change in color (either red, white or purple) or pain develops then go to A&E tonight. Otherwise you should get the hand examined tomorrow.