I have red or purplish dots on my arms, what is that and how can I get rid of it?

If they are located on your triceps then they are pimples. You can use a loofah with plenty of lather each day and they will minimize over time. I had pimples on my triceps. I made sure I scrubbed a little extra and they went away.

This isn't really an answer but I find that I have a few of these on the outer and inner sides of my arms. I remember seeing them more profusely on my grandma's arms and more recently a few on my dad's arms. I really think it's just a skin discoloration or a genetic skin condition. I don't think it's anything to worry about.