Can one injure their urethra or veins in the penis by using the squeeze method during masturbation? Squeezing under head during ejaculation?

Probably not... Squeeze technique to ease or abort imminent ejaculation is applied before ejaculation, not during ejaculation. The degree of squeeze for premature ejaculation should usually not hurt the urethra or veins. For effectively managing your sexual concern, you need a comprehensive evaluation and counseling plus other applicable measures timely. So, see doc of expertise for detailing.