My heating and cooling system went out yesterday during a storm and I found out that a 3 amp fuse in the system had been popped . So I replaced the fuse and the system keeps popping any 3 amp fuse I install.

I would start looking for damage or bare low voltage wiring. Most likely be on the exterior. Damage could have existed prior to storm but only shows up now that things are wet.
Squirrels, dogs and other thing sometimes like to chew on them. Usually, the wiring doesn't get along very well with lawn mowers and line trimmers.

I could not find any damage to any of the wiring. There was a power surge during the storm and now the system keeps popping the 3 amp fuse.

Disconnect low voltage wiring from unit outside. If fuse no longer blows the problem is in the unit. If fuse continues to blow, disconnect low voltage wiring from unit inside. If fuse no longer blows, problem is in low voltage wiring between the inside and outside units. If fuse blows problem is in low voltage wiring inside the house or the inside controls.