Do I have a personal injury case?

Yes, you should see a qualified licensed personal injury lawyer in your locale. Good luck.

I agree with Mr. Brinkmeier that you may want to consult in person (not online) with a qualified personal injury attorney. But I suspect you meant to ask "is there a case here that I can win?" And the answer to that question is by no means as clear as Mr. Brinkmeier's answer might suggest.

You'd presumably be suing the City of Houston or other local municipality that has responsibility for street maintenance. Texas law has become increasingly more unfriendly to premises liability claims of all sorts, and municipalities are particularly difficult targets to sue, with a set of special rules and procedures that protect them.

Running or jogging inevitably involves risks of injury of exactly the sort you apparently sustained. You describe the place where you injured yourself as one that had been "had been visibly breaking up," and that has been "slowing wearing away since I started residing here 10 months ago." This sort of statement suggests that you knew -- or, if you'd used ordinary care, you ought to have known -- of the danger of trodding there. And did you report the dangerous condition? Winning this sort of case requires a showing that the municipality knew, or in the exercise of reasonable care ought to have known, of the dangerous condition. If you knew of it but didn't demand the City to make repairs, the City will argue that you're more at fault than it. To the extent your injury was caused by your own failure to use ordinary care in avoiding an open and obvious hazard, your recovery may be sharply cut or even eliminated outright.

In any event: Get medical treatment. Consulting a lawyer before you consult a doctor will be portrayed as evidence that your claim is exaggerated or manufactured outright. And any lawyer will want to know how badly you're hurt and what your medical prognosis is, and what your past and future medical expenses are likely to be, before deciding whether your case is sufficiently attractive to consider taking it on a contingent-fee basis.

Sorry if this reaction seems bleak, but you should avoid lawyers who give you simplistic and one-sided evaluations that don't include an analysis of the likely weaknesses of your case.