Your bathroom is 280 CF if it has 8' ceilings. Your existing fan will completely change all of the air in 3.5 minutes.

Before changing the fan, I would check a few things first:

1. Is the bath fan venting properly? Do you see it pull the steam out? Is it possible that it's clogged, a flap not opening, etc?

2. Do you have a shower head that is breaking up the water too much? I installed a water saving shower head that generated much more steam than the standard head - in part because it broke up the water more and in part because I had to boost the water temp in order to feel the hot water.
I had to get rid of that water saving shower head - the extra steam was damaging my bathroom.

Thanks for the response, I went outside and I could feel the air pressure coming out the vent, I had taken the motor out and cleaned the fins a while back but it does not change all the air in 3.5 minutes. It takes about 20 mins. at least with the door open to clear out the bathroom. You said my bathroom is 280 CF, you mean I need a 280 CFM rated fan?

Do you have a gap under the bathroom door? You need a gap so replacement air can get into the room.

Alternatively, with a bit of luck, there's a fan upgrade kit that might fit your housing. Pull down the cover, measure the dimensions and go from there. One caveat is that sometimes they still don't fit even with the same dimensions. When this was the case, I was able to swap the old fan mounting bracket to the new motor assembly to get it in there.

It sounds like a pain, but it was still better than opening the ceiling to replace the whole thing, since I didn't have access from above. But if you do have access above, definitely swap out the whole thing.