You can see from other answers on this site that the word photon is used in many ways, and you see phrases like "the photon tranvels as a wave and interacts as a particle", and you get confused.
Now even before the photon comes to existence as a photon, its energy is stored in the electron field, the energy is part of the emitting atom/electron system, and as the electron relaxes, it transforms part of its energy to the EM field, and we say that the photon comes to existence. The photon, this QM phenomenon, the excitation of the EM field, as soon as it comes to existence, it propagates through space when measured locally, in vacuum, at speed c.
Now you mention the double slit experiment, and contrary to popular belief, the experiment is very well done emitting single photons at a time.
This is something beautiful about QM, this is what we call a photon, this QM phenomenon, that the laser is able to emit, one at a time, this quanta of light, is propagating through space, and we use mathematical models that model the photon as a wave when propagating.
Now it is very important to understand, though being counterintuitive, the photon does travel through both slits, and does take all possible paths. As long as it travels, it is best described by wave models, and it is delocalized.
The photons do not have a well defined trajectory. The diagram shows them as if they were little balls travelling along a well defined path, however the photons are delocalised and don't have a specific position or direction of motion. The photon is basically a fuzzy sphere expanding away from the source and overlapping both slits. That's why it goes through both slits. The photon position is only well defined when we interact with it and collapse its wave function. This interaction would normally be with the detector.
Shooting a single photon through a double slit
The only time we localize the photon itself, is when interacting with it, in this case whenever it hits the screen, and gets absorbed, that is when the photon ceases to exist, but its energy just gets transformed into the electron field again, becoming part of the atom/electron system's energy again.