I am so sorry you are dealing with this! The risk to health is beyond belief and to have so little support from your city council is even more exasperating.
As a member of the media (newspaper editor in Oklahoma) I can testify to the power of a sympathetic reporter and a well-written article.
My suggestion is to approach a reporter whose work you admire (be sure that you actually READ -- even better is to SUBSCRIBE to the local newspaper) and share with them the problem and how you have tried handling it on your own. This can effectively be done through a log of who you have contacted when, including their phone numbers, email addresses and other contact info, and what the outcome was of each contact. Not only will this serve as background material for the reporter, it can also help in the event of a lawsuit.
So, a few tips:
1) Get familiar with the newspaper and its staff by reading it, noting who it is that covers local news beat, animal issues, health and medicine, — any of those areas of responsibility might be interested in taking on this subject.
2) Keep a log of any and ALL communications, including date, time, place, subject matter, outcome, etc. -- using as objective phrasing as possible (we have to keep emotion out of our reporting, it helps if you can too). I suggest you keep a notepad by the phone, the computer, your writing desk, wherever the communication originates, to simplify the record-keeping process.
3) Always include a CC: or 2 (or more) when communicating. Whether this be to your veterinarian, attorney, husband, the other neighbours impacted by this sewage runoff AND the council member representing your district. It helps to convey that more than just one person cares about this issue and the noise level is going up fast and loud.
4) When you've done a little homework on the newspaper (they have the page space, time and ability to REALLY tell the story -- not just confine it to a 30-second bit as radio or TV would be restricted to) then send an email to the managing editor stating briefly the situation, including a pic or two, and asking if the power of the press can be brought to bear against a reluctant city council.
5) Throw in a few compliments about the newspaper, that you subscribe and rely on it for accurate information, etc. That will help separate you from the crowd of folks clamoring for a story to be done on their pet peeves. It also warms the hearts of those of us feeling like we are losing a battle to Facebook.
6) If at first you don't get a response then quietly and respectfully request a meeting with a reporter directly. Invite them out to see (and smell) the damage. Host a neighborhood meeting and invite the reporter to come and just listen...
Hope this helps. Sounds like it is guerrilla warfare now.
All the best from this Oklahoma news desk.