How can you file for yourself in a medical malpractice suit, if you haven't found a lawyer by the deadline to file?

Yes you can do this but medical negligence cases are very difficult even for the most experienced lawyer. It would be very difficult to represent yourself going forward. By filing yourself you stop the statute of limitation from barring your case but after that the procedural requirements, etc. would be very difficult for you to meet on your own. You do not provide any detail about what happened but if you have looked for an attorney and no one was interested perhaps there was no viable claim to pursue.

You can certainly pay a local lawyer to help draft a complaint so you can get it filed in time.