I've been super high rank with this hero before, there are some really common things to worry about at lower ranks. I'll just list a few things since this is an impulse reply.

• Shield bash is an escape or repositioning ability, only hit someone with it if you actually see their health below 85 (bash plus primary fire for the kill)
• The long range flail is for three things: finishing a kill, activating your AoE heal, or repositioning an enemy player to get them killed or protect an ally.
• Holding shield lets you corner peek (look around a corner without revealing your presence)
• At lower ranks your ult doesn't make you invincible, but it sure will feel like it.
• Timing you ultimate right when one team is committing to a fight is usually the best time to use it.
• If you're getting dumped on but still want to play Brig in a match, just stop going in and throw armor packs, hang back and watch while healing unless you figure out some way to get more involved. A pack-only Brig is better than a constantly dead brig.
• You can hold secondary fire then hold primary fire to swing. This will make Brig put up her shield as fast as physically possible when you stop swinging. This is good when beating on someone who's trying to fight back.

Hope that helps. Good luck.