|"every decent video card on line was showing me a minimum of 400 watts"|
I wrote this response about a week ago: When a graphics manufacturer recommends a minimum PSU wattage, it's for the enter system with the video card installed, not for the video card alone. The manufacturers realize that not all PSUs are created equal so they play it safe & over-recommend the wattage.
You should have waited for more answers. You didn't tell us anything about your 350W power supply other than wattage & wattage is no way to judge a power supply. And a decent quality 350W PSU is better than a cheap generic 550W. Hopefully the 550W unit you ordered is a reliable name brand with a single +12v rail of 30A or more, active PFC, 80 plus certified, & at least a 3 yr warranty? A decent 550W unit should cost between $50-100. Here's an example of a good one:
Here's an example of cheap junk:
The video card your ordered is way more than you need for the intended purpose. The Radeon HD4650 linked to by kuwese would have been more than sufficient & there would have been no need to replace the PSU.