I noticed salpingitis in one of my hens last year. This was before I was aware of the terms "lash egg" and "salpingitis." The kind folks here at BYC helped me figure out what to do. Thanks to them, she managed to survive and is probably near, if not at the top, of the pecking order today.
This is the thread I created last year. I found the replies there incredibly helpful, perhaps they might help you too:
https://www.backyardchickens.com/threads/hen-laid-a-hard-cooked-yolk-no-shell.1337314/
I don't believe salpingitis is contagious, but the pathogens that cause it may be. In my case, the hen that had salpingitis also had bumblefoot. It's possible that the infection moved from her foot. To provide better comfort and care and to prevent pathogen spread, I brought my hen indoors.
As coach pointed out here and in the linked thread, enrofloxacin (baytril) is most effective for this illness. I've used it to treat my first detected case of salpingitis and later used it to treat another hen that I suspected was in the early stages of EYP. Both cases had good outcomes. The dose I used per instructions from
@casportpony was 0.045ml per pound of bodyweight given twice daily.
In my case, I only had amoxicillin available and had to wait for the enrofloxacin to arrive in the mail. I followed the dosage provided by
@coach723 for amoxicillin (which is more readily available from pet stores as fish amox), which is 57mg per pound of bodyweight, given twice daily. I switched off of amoxicillin to enrofloxacin as soon it arrived in the mail. One course (5 days) of enrofloxacin and a lot of TLC did the job.