You may be suffering from little more than anxiety about your erection. When you say your penis tilts do you mean that the penis is unable to sustain an erection? If, so, you may wish to visit your gp again, as many factors can affect erection.
If your penis is tilting at an angle whilst fully erect, you may be suffering from peyronie's disease although this seems unlikely from your description.
The issue with your vein is probably not a cause for concern as the genital area is blood-rich and veins are more prominent in some individuals than in others.