Consider a Photon from Sun and travels with a velocity $c$. Now think we are that photon. For us, it looks like Sun is moving away from us with a velocity $c$. So, why don't we get attracted back towards Sun, because the mass of Sun would be infinite for us since it moves away from us with a velocity $c$.
You have completely mixed the modern and classical concepts of relativity. If you're talking about mass increment, you shouldn't calculate speed of Sun based on absolute time & space notion.
For you as a photon, space will be contracted to zero and time will be dilated to infinity. So, you can't calculate a speed (which is a time-like spacetime event) of Sun.
While its a nice satisfactory explanation, its not the real one.
When anything moves at the speed of light, all of our physical models break down. If you were to watch a spaceship speed up to the speed of light, you would see a clock on the ship slow down and come to a complete stop when it hit the speed of light (assuming you could even see it at this point). The ship would also contract so much in the direction of motion that it would become infinitesimally small and, when it hit c, it's length would hit zero. As a result, matter cannot ever reach the speed of light (as far as we know).
It is a common misconception that mass changes when you travel at relativistic speeds, but this is not actually the case. The kinetic energy of an object increases relativistically, but the physical mass of the object (and, therefore it's gravitational effect on surrounding spacetime) does not actually change.
By our current notion of relativity, it is completely possible that there exists another universe within our own, in which photons are at rest and we are moving at 3e8 m/s and have energy but no other way of interacting with the type of "matter" that exists here. Our world is inaccessible to this one and vice-versa. There could be completely different laws of physics in this parallel universe, we have no idea because it exists (or doesn't) in a singularity.