Is there a time limit to file for SSI or SSDI?

Yes. SSI benefits start accruing the first full month after you apply, so you lose money the longer you wait to apply for SSI. Since SSDI allows you to go back and get benefits for up to one year before the application date, there is less of a time limit. But, you should still apply as soon as possible once you become disabled. Also, for SSDI, you must (usually) become disabled no later than five years after you stop working fulltime.