Good advice to get it checked out, that's always the best choice with most mysterious symptoms.
Varicose veins typically aren't acute, and MOST times do not hurt. Plus, you would likely see discolorations or something along or around the vein.
A DVT (deep vein thrombosis) is the clot that ckissinger is talking about. Clots in the upper extremities are pretty rare, and usually they are VERY painful, and accompanied by redness, swelling, and the area will feel warm or hot to touch.
It could be a strained muscle, and you are relating to the "vein" because that's the location of the strain.
If the pain isn't severe, and you don't have any numbness or tingling in the lower arm, or hand, you can probably give it a day or two to see if it resolves. You could try some Motrin or Tylenol, along with alternating heat and ice too. If it is a muscle strain, those interventions will help.
Good luck, and remember , like kissinger said, check with your doctor if it doesn't start getting better.
I would have it checked out...It could possibly just be a 'vericose vein' but I would be concerned about a blood clot. I would see your doctor just to be sure. Especially if you have not recently injured that arm or anything like that.