What would happen to the boiling point if the atmospheric pressure would begin to rise?

A liquid boils when the average kinetic energy ( as measured by temperature) exceeds the kinetic energy of the environment above the liquid ( As measured by pressure)

If the pressure increases the temperature of the boiling point increases. This is why food cooks faster in a pressure cooker. The increased pressure increases the temperature speeding the cooking process.

Conversely cooking food at high altitude takes longer. This is because at high altitude the pressure is less. The less pressure the lower the temperature of the boiling point. The lower the average temperature the less kinetic energy available to cook the food.

By definition, the boiling point is the temperature at which the vapour pressure of a liquid is EQUAL to the ambient pressure, and bubbles of vapour form directly in the liquid.

The #"normal boiling point"# is specified when the ambient pressure is #1*atm#. And thus we use vacuum distillation to lower the boiling point so that we can get an otherwise involatile liquid to distil at reduced pressure.

And should we increase the pressure, we have to consequently INCREASE the temperature of the liquid so that its vapour pressure becomes equal to the increased ambient pressure.