Protruding veins is not uncommon so the bulge probably isn't serious.
I suspect that it is something you've had for some time but not noticed until the recent doctor visits and which is now being magnified by your anxiety.
People with some types of anxiety can become fixated on what they perceive is an abnormal physical symptom. Some constantly monitor their breathing, others focus on heart rates or blood pressure, etc. Given that at the root of most anxiety is concerns of dying this is not surprising.
Consulting your doctor about this might be the easiest way of dispelling your immediate concerns. If you are not being treated for the anxiety that might also be a good time to discuss this with the doctor too.
I see from a subsequent post that you were worried about this being a blood clot (thrombosis) with the possibility of stroke.
Blockages in surface veins are unlikely to cause problems simply because being on the surface they are able to bulge. Varicose veins being an example. People often have these for decades without drama.
The ones that cause problems are in the deeper veins. The usual sign of a clot in a limb is intense pain followed by the affected limb going cold beyond where the blockage is. They need urgent medical attention.
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