Hi,
Your post should probably be in the dermatology community. Maybe MedHelp can move it. But like the poster above mentions, tanning beds can lead to skin cancer - not sure if you are aware but they have the same properties as the sun and can lead to Melanoma, etc. I have had a Melanoma. This is something to think about.
C~
They look like broken capilliaries. Have you been carrying a heavy bag or lifting a heavy weight? I get those when I've exerted my arms or carried a pack or something.
Please think twice about tanning beds. If you're worried enough to visit a skin cancer forum you might be worried enough to protect your skin from tanning. They're not safe.
Take care.