I have them also, I believe they are called petechiae and are quite harmless I understand. They are actually tiny haemorrhages (bleeding under the skin) that are probably caused by the exercising of that muscle, you did mention you go to the gym.
I must say I am pretty sure that I know what you are talking about but I have yet to find out what they are from.
The red dots could be caused from irritation from your clothes or working out. Have you noticed when your working out that your rubbing one of the machines, or maybe your bicep and for arm rubbing together? Remar