But what more can I honestly do, I just feel like I've failed these chicks.
Concentrate on the fundamentals. What is the temp under the brooder plate? Not the temp of the plate itself, but the temp of the bedding below the plate. Mind you, I only have used heat lamps, but I have had success with with 95F for week one, 90F for week two, 85F for week three, etc... But I live in northern Minnesota and my brooder is out in an unheated garage, so heat is always of prime concern to me.
Again, I have never used a brooder plate and that might change the way you need to look at temps. However, I believe a hen's body temp is 105F, so take that into consideration if the temps under the brooder plate are significantly cooler. Even with heat lamps, I tend to err on the side of a bit too warm thinking that the chicks can run out into the cooler part of the brooder if needed. Or they can rest in an area half in and half out of the heat lamp. But you cannot create more heat out of nothing.
I mention this because you seem to be worried about the chicks catching a cold, with all the sneezing and you are looking for a runny nose. Just do what you can and try not to put so much guilt on yourself.
Have you decided if you are going to get more chicks? I think you mentioned that before. Personally, I'd get more than the 3 chicks you currently have as I think flock animals just do better in a flock. It does not take more time to feed and water 10 chicks than it does to feed and water 3 chicks. Also, as I mentioned before, a loss of 1 or 2 chicks out of 10 is less damaging to my psyche than losing 1 or 2 chicks out of 4. Right now you are stressing over the well being of one or two chicks that are not as strong as the others. When I get more chicks to care for, I tend to focus on the overall health of the flock and not beat myself up over any one chick.

But I have raised small animals since I was a young teenager, and over 50 years, maybe I have built up more defenses to protect myself from the heartache of a sick animal or even losing some along the way.