See a dermatologist about yeast infections, or HPV, or Fordyces condition (which is not contagious)
Yes, you should see a doctor, not because it's serious and contagious, but because it almost certainly isn't, and only way you're going to know that for sure is to have a skin doctor take a look. Nothing to be embarrassed about. Lots of people have bumps on the penis like the ones you describe, so go and find out if yours are normal too.
Take care.
Dr. Rockoff