I hate that I have to baby my 96 mustang

Could it be from my engine

Previous owner probably did not maintain the cooling system and used tap water instead of coolant. My concern would be the heater core is in the same condition. If mine, I would consider a chemical flush of the cooling system to remove rust and contaminants from the block and heater core.
Hopefully some of the real mechanics (Iā€™m not) will respond.

That would be one way to go, and if you make sure you get all the chemical flush out of there, Iā€™d be okay with it. Iā€™m not a fan of chemical flushes because Iā€™ve seen someone misuse a chemical flush and damage his engine by not following the instructions (and because Iā€™d hate to accidentally damage my head gasket with an acidic chemical flush - which Iā€™m told shouldnā€™t be an issue, but I prefer to err on the side of caution).

Another way to go would be to assume the heater core is as bad as the radiator was and replace it now. Then Iā€™d flush the cooling system with clean water, get as much of the tap water out as possible, and fill the system with either premixed coolant or a mix of concentrated coolant and distilled water (using universal yellow/green coolant on this car since itā€™s out of warranty) . After that Iā€™d drain and refill the cooling system every two years to make sure the corrosion inhibitors are fresh. I might also proactively replace the water pump, depending on how difficult the job is and how much it might cost.

Iā€™m not a real mechanic either, but thatā€™s how Iā€™d approach the issue of what I found and what it might mean for the rest of the engine.

I agree with your comments, just hoping for OP the heater was still okay since dash has to be removed to replace heater core.
As far as a flush I was thinking more of the mild flushes sold. At on time oxalis acid was sold as a flush but I believe it is no longer available due to the problem of completely getting it out and neutralizing the acid.

So, how deeply was it immersed in the floodwaters?
Floodwaters arenā€™t bathwater. Theyā€™re full of all kinds of matter much of which is highly corrosive and much of which is just plain disgusting, passage-clogging gunk.

I hate to say it, but I think that radiator core is a sign that your problems have just begun. I wish you all the best.