This could be the result of a few things. First, are you certain that the AC system is fully charged? If it fails to actuate the compressor, the fan won't turn on. Here are a couple links. The first one discusses common issues with AC not working. The second explains how to charge the system.
Let me know if that helps or if you have other questions.
Joe
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Tuesday, October 1st, 2019 AT 6:27 PM
URSULOROBLES
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With engine running, the low side is high and high side is low, when A/C is on, the compressor clicks on and low pressure goes down to 100, but the fan does not come on. Therefore the A/C compressor disengages and vehicle gets hot.
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Friday, October 4th, 2019 AT 6:41 PM
JACOBANDNICKOLAS
MECHANIC
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Welcome back:
If the low side goes down to 100, that is extremely high. The idea that the low goes high and the high goes low, I suspect the compressor is bad. If the low side goes down to 100 where does it start?
Joe
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Friday, October 4th, 2019 AT 9:24 PM
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The A/C low side is over 100, compressor clicks on with no cooling fan, and low side pressure goes down to 100 and compressor shuts off.
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Sunday, October 6th, 2019 AT 12:25 PM
JACOBANDNICKOLAS
MECHANIC
109,724 POSTS
Welcome back:
I suspect either the system is either over charged (high pressure switch turning it off) or the compressor is bad. Even under extreme conditions, for example at 110°F low pressure should be under 60. Could you have over charged it?