the precipitate dissolving with addition of HNO3 confirms it is phosphate. Phosphate is unable to form precipitates in a low pH because the PO4 3- reacts with H3O+ (due to the acidic environment). This makes HPO42- (PO43-(aq) + H3O+(aq) < -- > HPO4 2-(aq) + H2O(l)) and also can make H2PO4 - as well by a further H+ being accepted.
These two forms of HPO4 2- and H2PO4- when they form salts are relatively soluble in comparison to phosphate and so that's why when these form after HNO3 is added the precipitate dissolves.
It can't be the chloride one because if you add HNO3 on top of that it's not going to dissolve the precipitate