I didn't realize they sold these to the general public anymore. In all the breastfeeding training I've attended (I contracted with our local WIC program as a lactation consultant), we were told to never recommend a mother use a BF shield without the supervision of a lactation consultant. It can be incredibly difficult to wean the baby from the shield once s/he is used to it.
We always recommended hand expressing enough milk to soften the areola and allow baby a better latch. Be sure to save what you express in the freezer.
You can also pump a little before each feeding, but BE CAREFUL how much you pump because you could end up adding to the problem! The more milk you take out, the more milk your body will make causing even more engorgement.
If you are uncomfortable you can wear cool cabbage leaves in your bra. I know it sounds funny, but it's cool and contains a chemical that let's the breast leak enough milk to become comfortable. If you crumple the leaf before you use it, it will release more of the chemical.
A cool washcloth over the breasts feels good, too. They also make cool packs you can put in your bra if you get desperate.
Some ladies have had success using a breast
shell (different than a shield). You wear it in your bra prior to feeding baby and it causes the nipple to stick out more (milk will also leak into the shell).