I purchased a Shield .45 in February. Initially, I had the same problems you are having. It shot 3"-4" left at 15-20 yards, and had persistent failures to feed, where the bullet tip would get hung up just below the lower feed ramp. Here are my suggestions:
1. Shoot from a bench rest.
To check if my shots to the left were caused by my grip or the sights, I shot my Shield from a bench rest. The shots continued to go left, even though the Shield was essentially being held by the rest, confirming that the front sight was off. One of the range officers kindly adjusted the sight until the shots were centered. Having a sight adjustment tool helps, as the Shield's front sight is notoriously difficult to move. The rear sight is not adjustable. I've had no shots-to-the-left problems since.
Now if my initial shots from the bench had been centered, then I would have known that the problem was caused by my grip.
2. Polish the lower feed ramp.
I got some mild car polish and rubbed a small amount of it all over the lower feed ramp area with a cleaning patch. The lower feed ramp is the one that remains in the grip assembly after you've removed the slide. I polished both the ramp and the vertical wall just below it where the bullet tips would hang up. I used a clean patch and Q-tips to remove the residue. The ramp and wall felt notably slicker after that. I did not polish the upper feed ramp (which is attached to the barrel) because it was never involved in the failures to feed.
3. Clean the insides of the magazines and the followers.
If your followers are not sliding smoothly up and down the insides of your magazines, they could cause jams by not placing the cartridges in the proper position for loading. After cleaning, push the followers down several times to make sure they're sliding smoothly without hanging. Lubing the inside magazine walls is usually not necessary, and should be done only as a last resort. If you do decide to lube, use only a very light application, and then buff the heck out of it after that.
Since polishing the lower feed ramp and cleaning my magazines, I've shot over 500 rounds with no failures of any kind.
4. The 7-round magazines are "unique".
The Shield .45's 7-rounders have a unique base plate design that makes them difficult to reassemble, at least initially. Use the Forum search feature and you will find some excellent tips and at least one video that will be very helpful. Once you've done a few reassemblies, it becomes fairly easy.
5. $20 per box .45 ammo is not "cheap".
Search the internet, and you can find quality .45 target ammo like American Eagle and Winchester Service Grade for $15-$16 per 50 round box.
My Shield now has about 2500 rounds through it, and I love it. It is reliable and very accurate and has joined my trusty M&P 40 compact as my second carry gun.
Welcome to the Club!