Help, need ideas for a software to keep animals from euthanasia!

Hello, I'm a marketing professional who volunteers for a rescue group who tries to save dogs and cats from euthanasia at 3 rural county animal shelters. Here's the process - we get a daily intake list, descriptions and pictures from each shelter. We post these on our Facebook page and ask for pledges for each animal (we don't handle the money). We (the volunteers) then comb through the hundreds of comments and likes to find pledges for each post. Once we identify a pledge we manually record it in a google sheet at which point we have to find a rescue group to take the dog or cat. The more pledges, the more likely a no-kill rescue group will agree to take the animal to try to find a forever home. There is a time crunch involved. These shelters only allow animals to stay in the shelter for a short amount of time before they are killed. One is 3-5 days. Every moment spent administering the system is a moment lost in the process of saving the animal. This is a 24/7 process, and it's never-ending. It's arduous and manual. I would love to speak with a product or software developer for a better and faster way of doing this so we can save more lives.