Thank heavens you went out and found her!
ww, THAT'S what you have to focus on...you were attentive and aware enough to notice there was something peculiar...and you checked it out. It is totally understandable that initially your brain interpreted the sounds as strays; you know it's said, "when you hear hoofbeats in the distance, think horses, not zebras!"
Poor elderly neighbor! It's maddening how many elders have those LifeAlert things...and don't wear them...or let the battery die! My own parents were prior offenders themselves. 
In a slightly similar situation, my father damn near froze to death (literally) on their driveway several years ago after falling on the ice in the dark about 200' from the house. He's got bad arthritis in his knees, his glasses went skittering off into the dark, he didn't have gloves on because their unruly dog had chewed up every pair he owned, he didn't have his LifeAlert pendant....AND the wind chill that night was -18F.
It took him 2 hours to crawl to the front door; my mother (w/advanced alzheimer's...yeah, she shouldn't have been left alone in the first place...but another story) wouldn't let him in because "YOU'RE not my husband!!"
If the guy that plows their drive hadn't come by, totally by chance, and seen their car left at the head of the drive...and most importantly, checked to see if something was amiss, I truly believe my father would have died from hypothermia. As it was, he wound up hospitalized for 2 weeks due to bad frostbite on all 10 fingers.
You checked, that makes you an angel.
I can understand the guilt part, and speak from experience about needing to focus on the fact you checked. Earlier this summer I'd heard yips and small-dog-sounding yipes most of the afternoon (in the heat but at least it was overcast). When I walked up to the street to get our mail, I noticed the young husky who belongs to one of the people who lives near us was sitting in an odd, crouched position. (Difficult to see clearly, as it is through a little curtain of trees, grasses, and undergrowth.)
It just didn't look right, and I hopped in the car and went around. Come to find out that this poor dog had her leg just terrifically caught in the stupid coated wire cable this woman tied her out with on a run. A dead branch had fallen onto the cable, the dog must've gotten scared...whatever, it wound up being a tourniquet repeatedly, severely wrapped around her leg, with the branch serving like a bit of a Spanish windlass. Her lower leg and paw were so swollen I thought she'd wind up having them amputated. 
The cable was so incredibly tight and cut so badly into this poor baby that my H had to bring steel cable cutters (thank God we are 'tool people'!) and make 3 cuts before we could free her. Ultimately, she recovered okay.
I felt just horrid about this poor sweet dog suffering in a torture-worthy configuration and posture all afternoon. Just sick over it. However, by focusing on the fact the positive side of the story, over time I was able to put it in perspective. No one else even took note of the dog's cries or posture.
Long-winded way of saying you done good, and let go of the guilt. 
