I just replaced the starter on my daughters 1996 Honda Accord it started overheating and shutting off she put antifreeze in the radiator but it continued to smoke and shut off again now it won't s

If the smoke is white ,it's water (head or gasket)
Timing belt will shut it off completely.
Can't see any way the starter could have anything to do with it.
However if it has a head gasket problem,hydrostatic lock can
make a good starter look bad(,water will not compress like air)
so if there is water in a cylinder the engine won't turn over.
If a head gasket is bad there will be white smoke out the
tailpipe and bubbles coming out of the radiator (cap off while
cold)

If a mechanic told me the starter was making my car overheat, I would take my car somewhere else. Honestly, that's just ridiculous.