"Floods all around the world" and "floods over all the world" are *not* the same thing.
The melt of the ice sheets caused many large, local floods from melt water trapped between land features and ice sheets where either the ice, or the land forms failed releasing locally catastrophic floods over hundreds of km.
Here's an article summarizing such floods and listing many examples. Note that none of them happen far from the glaciers.
Glacial lake outburst flood - Wikipedia
One particularly spectacular example is the Missoula floods in the Pacific NW of the US.
An Introduction to the Ice Age Floods – Ice Age Floods Institute
The "Black Sea Flood" (I have the book here somewhere...) is caused by
1. the sea level *dropping* during the ice age as the water was redistributed into ice sheets
2. The Mediterranean Sea dropped below the level of the straight of Gibralter isolating it from the oceans, causing it to drop even further.
3. The Black Sea was cut off from the Med.
4. The Oceans and Med started to rise, and overtopped the land separating Med and Black seas. This rush of water caused the Black Sea to rise fairly rapidly, but in a fashion that would cause to shore to expand at roughly a walking pace.
5. The people abandoning their villages on the dry bottom of the Black Sea carried out stories of a mass flood that forced them out of their villages.
Black Sea deluge hypothesis - Wikipedia
There are problems with this being the origin of the Noah flood myth. There is no rain, and no need for boats to save anyone or animals. It fits much better with a massive flood in an enclosed river basin.