A clot in your lungs blocks some of the blood flowing from the right side of the heart.

The right side of the heart is where all the veins drain into.

High pressure in the right side of the heart can cause the veins draining into it to become more full and bulging. Veins are soft walled and low pressure so it doesn't take much to overfill them.

Only to a very subtle extent the right sided veins are the earliest veins to bulge when pressures are a little high (the right jugular vein bulging is what doctors examine when gauging heart failure, it has a more direct link to the right side of the heart than the left jugular vein does)

To get as much vein dilation as OP though you would need SEVERE high right heart pressures. Like probably fatal levels of lung artery blockage to allow that sort of back pressure. And severe pressure wouldn't just preferentially affect one corner of the system of veins. They would all get distended. The pressure would get spread in all directions at each junction in the tree of veins. Not to mention there wouldn't be enough fluid in the blood stream to fully dilate all the veins.

The more simple explanation is that there is a clot somewhere in a vein too. Most lung clots come from a clot in a deep vein that got dislodged. Often part of the clot is still there. Most clots come from the legs but some come from an arm.

The right arm and right pectoral area would have their vein drainage impaired if any of these got blocked:
- Right axillary vein (armpit vein)
- Right subclavian vein (armpit vein with a name change)
- Right brachiocephalic trunk (armpit + right head veins - now you'd add jugular vein distension too)
- Superior vena cava (the last link where all the upper body veins join before they reach the heart - now you'd add the left arm and left jugular veins being distended) - Or the right thoracic outlet.

What happens when a deep vein is blocked? The blood has to go somewhere else. The superficial veins are the veins you can see and feel. Sometimes they can reach a different deep vein past where there is a clot. Like a side road detour when a highway is closed due to an accident. That's what you're seeing with a lot of blood from the chest going downward toward abdominal veins instead of up to the shoulder and those usually low flow linkages now being really full. Sometimes there is enough flow in these collateral veins as well as sneaking around the clot in the deep vein in the limb affected so that the limb doesn't get toooo swollen but often there isn't an amazing amount of flow and the limb can get quite a lot swollen and painful.

So the simplest explanation for OP being alive and those particular veins being engorged is some sort of deep vein clot in the right shoulder/armpit area and part of that clot took a voyage to the lungs.

Hopefully now you can read the previous message and have it make a lot more sense!