Can an object grow past the schwarzschild radius?
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To start off with you don’t quite understand what the Schwarzschild radius is. It is not some limit of size where an object gets bigger and bigger, creeping up on it from below and when it is finally reached the object becomes a black hole.
Instead the Schwarzschild radius is the radius *below* which the force of gravity would cause it to irreversibly collapse. There would be a star which is balancing the force of its own gravity pulling inward against the force of the fusion in its core pushing outwards, until it runs out of fuel and gravity can crush it into a black hole.
Or you might have a neutron star which is cooled and prevented from further collapse just by neutron degeneracy pressure (you can’t pack neutrons any closer together) but that if somehow it was compressed into a smaller radius overcoming that pressure, below the Schwarzschild radius it would collapse into a black hole.
Based on the above what you really should be asking is if something could grow larger while **below** the Schwarzschild radius. And no, it can’t. Gravity pulls on things with mass, and *light doesn’t have mass*. An asteroid being tugged into a curved path by the gravity of a massive star is not the same thing as what happens when light’s path is bent by a massive object. Instead what is happening with light is that the light is not affected by gravity, the *space itself* is. Space itself is bent by gravity and light just follows along what to it is a straight line.
When a black hole is formed light is unable to escape not because it can’t claw itself away from the force of gravity, but because gravity warps space itself to the extent that **all directions point inward** to the black hole. There is no direction that light or anything else can travel to move away from deeper into the black hole so we can be certain it can’t become larger. There is literally “no way” for that to happen.
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