Hi
From your description, it sounds as though the damage may actually be to your lower back rather than to your hamstring, and that the pain you're feeling is a sciatic nerve stretch rather than a hamstring stretch. I'd suggest spending a couple of weeks stretching out your low back to get the joints moving again properly, and to allow any nerve irritation to settle.
Two exercises I'd suggest in particular:
1. Lie on your back on the floor. Pull your tummy in, and bring one knee up to your chest, and then the other. Hold your left knee in your left hand, and your right knee in your right hand. Cross your ankles and drop your knees apart. Relax your tummy. Use your arms to gently rock your knees in very small circles and up and down, and see if you can find a sore spot anywhere under your low back or pelvis. If you can, focus your rocking motion on that. If you can't, just keep rocking *gently* for a couple of minutes. I really do mean *gently* - if you are vigorous, your back muscles will kick in and prevent you from stretching out your joints and ligaments. Then after a couple of minutes of this, pull your tummy in again, and lower one foot to the floor and then the other.
2. Take a yoga brick or a pile of books about 7cm high. Start as you finished the last exercise - lying on your back on the floor, with your knees bent and your feet on the ground. Squeeze your knees together (this activates your buttock muscles) and roll your way up your spine, lifting first your bottom, then your low back, and middle back, until you are a straight line from knees to shoulders, with your weight just on your feel and shoulders. Slide the brick in under your bottom (*not* under your back) and lower your bottom down to rest on it. *Slide* (don't lift) one leg at a time out away from you so that you are in an arched position over the books, and let all your muscles relax. You should feel a stretch, and it may be uncomfortable. This is ok! Hold the position for 30-60 seconds, then *slide* one foot back up towards you and then the other. Squeeze your knees together, lift yourself off the block and slide the block away. Lower your bottom, pull your tummy in and repeat exercise 1.
Do the whole thing 3 times, i.e. exercise 1-2-1-2-1-2-1. If you do this every morning and night for the next 2 weeks, I think you will find that your hamstring/sciatic problem is significantly better, and then you can start stretching again. Stretch it by sitting on a table and swinging your legs. You've already found that is a more effective stretch for you than a straight leg stretch.
Hope that helps!
Nell