Bore sighters are an approximation at best; particularly with handguns. "good and parallel" as you mention is probably not the right solution. Others have mentioned how to change your sights, but before you do that I suggest a little more investigation.

Handguns are super-sensitive to grip. A loose grip may translate to more muzzle flip and a high impact. The reverse can be true too. You may also be flinching. With just a laser in the gun, you know it won't recoil so your hold is steady. With real ammo, you may be pulling the gun low on firing. Maybe getting someone else to shoot your guns would be indicative of what's going on. Or, try shooting off of sandbags.