The ACT test is tomorrow, and my friend has it on the same day as me, but I'm not going to remind him.
That's a big test. Why would you hide it from your friend?
I've been thinking about it and I might not be up to the task of taking the test
It is understandable that you may think you are not up to the task of taking the test but you should not hide the fact that there is a test tomorrow from your friend. Friends are expected to help each other and it is rude to withhold important information from them.
I'm not going to tell him because I'm afraid he'll let the cat out of the bag and tell other people, and then I will feel extra pressure because they know.
You shouldn't risk your friends suffering severe consequences from missing the test just because you are nervous. If he is really your friend, don't you want to make sure he does as well as possible? Maybe if you help him by reminding him, he can help you study in return.