OK, that is your suspensory ligament and everything is normal. It is just that in that stretch position, you are putting it under maximum load. So I would say you are doing the right thing, but just don’t pull so hard and you should become a little more accustomed to it as you get further conditioned to the stretch. You can also use other stretches at different angles that are more comfortable as you already mentioned.
Edit: On further investigation, I think that may actually be your fundiform ligament which is a group of 3 ligaments: the fundiform ligament of penis, suspensory ligament of penis, and arcuate pubic ligament that attach your penis to the body. Learning something new everyday myself! :)
Here is an illustration showing the fundiform ligament, that I believe is what is also showing in your attached pic.