Your case? ...as in for your defense or are you actually wanting an attorney to represent you because YOU slipped and fell while in jail? If the later is the issue, then I really think you're barking up the wrong tree. People slip and fall all the time...it happens...and yeah...it bites, but you pick yourself up and keep going.
No attorney will take your case, because they might feel that's an attack upon the jail, or your just doing that for money. Now, I'm not saying you are, but some attorneys will look at a case from every angle to see if they can win the case. Most attorneys won't take on a case if they feel like they can lose. My mom and dad, and my girlfriends mom are lawyers. They've had cases similar to this one and loss. They never took on a case like those again. In one case there was a leak in one of the cells, they believe it was coming from the toilette.The case was thrown out because of lack of evidence.
What next! You want to sue the jail because YOU slipped and fell! Next you're going to sue the cop because if he/she didn't arrest YOU there wouldn't be a slip and fall issue! Then you're going to sue your teachers because if the had taught YOU not to commit criminal acts you wouldn't have been arrested, booked in jail and fell! Lastly you can sue your parents for having the physical relations that brought you into this world. Grow up, live with it, people fall every day!
It really depends on why you slipped and fell and if there was negligence on the county and sheriff's part as to why the slip and fall occurred. Also government officials do have a level of immunity from being sued when carrying out their official duties. If you have consulted a handful of personal injury attorneys and they have all declined to take the case, most likely you have a weak case and/or there government immunity issues the attorneys do not feel is worth the hassle.
Since you cannot force an attorney to take your civil case, you can always try to take the matter to court yourself. Naturally, you will be required to follow all the rules of civil procedure as if you were a lawyer so it will involve a lot of research and work.