I think where you are going wrong is "your time freezes".
What this means is that if you have a clock on your hand, you will see your own clock tick normally (whatever speed you move with), but far away observers will see your clock on your hand to tick slowly.
In your case, the EM wave traveling from the Sun will travel the Sun Earth distance in approx 8 minutes seen from Earth (on a clock on Earth). Now you could ask, but how much time passed on the EM wave's clock. Now the problem is, as per SR, you cannot ask that question, because EM waves do not have an inertial reference frame. Nothing with rest mass can travel with speed c. But theoretically you could say that the EM wave's clock stopped (as seen from Earth).
Now you could ask what neutrinos' clocks coming from the Sun will show. You will still see approx 8 minutes pass seen from Earth (on a clock on Earth) until the neutrino gets here.
But if you were traveling with the neutrino, you would see your clock tick normally, but only a fraction of that time would pass on your clock until you would get here.
The problem is you think the way around, you think that normal spatial speeds are the ones we are experiencing. That is not right, because the normal speed is the speed of light, and everything is relative to that.
Anything without rest mass always moves in space with that speed. In the time dimension that particle is not moving. To start moving in the time dimension and start experiencing time like we do, you need to gain rest mass. Now it is because the universe is set up so that the 4 speed vector (x,y,z,t) has a magnitude always c. Now if you slow down in the spatial dimensions (by gaining rest mass), to compensate, your speed in the time dimension will start to change. You will start moving in the time dimension.