Based on your description it sounds like you are trying to measure resistance while the circuit is hot. Generally not advised. If so, what you may be seeing is the resistance increase slightly as the fuse gets hot. If you are measuring votlage drop, that's OK and the explanation is the same.

Take a look at this overview of the charging system power flow.
I think what has happened is:
1. the battery did not get sufficiently recharged.
2. as the battery voltage decreases, the voltage regulator tries to have the alternator supply more current for recharge.
3. 20 amp quick fuse blows immediately under the larger load.

If so, then everything should be back to normal after recharging your battery with a charger and installing a new fusible link. You'll have to dig through the service and parts books for the correct amperage for your car's fusible link.