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The a/c and fan issue would be unrelated in this case.
You don't mention how much refrigerant you added or what the pressures were before and after charging. If the charge is still low then the compressor may engage but not cool, especially when it's 93 degrees outside. Charging without a recovery machine is pretty imprecise, but shoot for a low side pressure of around 40 PSI on the low side if it's 90 degrees out.
The cooling fan issue is being caused by a bad cooling fan relay or a short on it's control circuit. This is a solid state relay that controls the fans with variable speed and it gets warm during operation so it's mounted to the sheet metal under the right radiator support. When this type of relay fails it will often cause the fans to run constantly unless the battery is disconnected because it receives a power feed all the time.