I have created a custom apex class that makes an HTTP POST call using callouts. Right now I have it running on a schedule using an @future method. This is working fine, but I actually want to connect this to a screen that a user can enter some parameters and then this class would run on demand and be set up to run on a schedule. Is it possible for me to create a screen to do this?
The answer is "yes". There are a number of different ways to deal with it, depending on the UX you want, how this process should be initiated and the level of coding you are happy to do.
My immediate recommendation would be to use a Screen Flow (this is covered in the Trailhead for flows), perhaps initiated from a Lightning Action that you add to the global actions or some other place. This avoids writing much code. You can create a screen with the inputs needed for the values you want, and update your code to support an InvocableMethod that takes the inputs from these as its parameters and then invokes your Future method to do the callout (I'm not sure if you need to separate it into a future from an invocable method - you can research this).
The alternatives involve more coding (e.g. a visualforce page or some LWC component you add to an app or home page, for example).