Up to date on your shots does not mean all shots completed. For young puppies most trainers will take them after their second puppy shot. Please for the sake of your puppy do not wait another month to seek out positive reinforcement trainers in your area. Read the American Veterinary Society for Animal Behavior's position statement on early puppy socialization, http://www.avsabonline.org/avsabonline/images/stories/Position_Statements/puppy%20socialization.pdf
Your puppy needs to learn impulse control, throwing tantrums when one doesn't get what one wants shows a lack of impulse control. View the video, Its Yer Choice on YouTube,This is one way to start training impulse control. There are many others but you really should be in a training class so you can have someone help you see how they work and what you should expect.