Do I have bumps at the base of the penis?

Based on your description, it seems like you may be experiencing irritation or ingrown hairs around the base of your penis after shaving. To avoid this in the future, it is recommended to shave in the direction of hair growth and not to repeatedly shave the same area. Consider using an electric trimmer instead of a razor, and apply a fragrance-free moisturizer after shaving. Avoid using deodorant or scented soaps in that area, and gently pat your skin dry after showering. Give these tips a try for 10 to 14 days and see if they improve your situation. If you have any further questions, feel free to ask.