Welcome to Knitting Help!
The cable actually look quite nice. Yes, loosening up on your tension will also help with the tightness on the left of the cable and looseness on the right. You don't need to pull the first two cable sts tightly up to the sts on the right needle. You can leave a small gap at this point.
If you find that the stitch on one side of the cable becomes too loose, there are some solutions for that here