Aids is just said by trolls. Him coughing up blood actually confirms it's not Aids, since that's not a symptom.
If you look just at his condition and symptoms, it most clearly resembles Tuberculosis if you want to equate it to a real life illness.
If you want look at it as symbolism, it represents the amount of suffering he went through and heart break.
If you want to look at it objectively, it was just a plot device Kishimoto came up with so that he wouldn't be able to spam hax techniques. Which is clearly the case.
U_U