Last year while training for a "Workplace Challenge" race (about 3.5 miles) I was wearing shoes that were probably a half size too small for me. For my "normal" runs those shoes were OK, but I was really trying to push myself in the last two weeks leading up to the race and during the race itself. After the race I started having pains in the back of my heel that flare up after I run. Based on doing a lot of Google searches for my symptoms, I'm pretty sure that I gave myself bursitis in my heel. MY problem is, I don't have the patience to really let it heal up properly. I rest for a while, then I go out and run and it flares up again. I did a half marathon in January, and I couldn't walk right for a week. One thing that I found that helped was rolling Biofreeze gel on it.
I just did a 10k race last Saturday, and thankfully my heel didn't flare up this time. So it looks like I'm finally pretty much over it. But I don't think it would have hurt me from July 2018 to June 2019 if I just had the patience to WAIT and give it time to heal before getting out there and running again.
TLDR: Don't sprint in shoes that are too small, even if you can run slowly in them with no problems. Don't keep running on your regular schedule if you have a nagging heel injury...give it time.