So I used to be into amp modelling but I wonder if you can do that with a computer program. Like get a sample recording from another guitar and then fix that to your guitar input into the computer so that when you play it sounds like the example that you gave it.
Some products offer a "Tone match" feature, which seems to be what you are looking for : you feed the product with a isolated guitar sound and it tries to match that tone.
It won't be perfect and you still have to work a little (like choosing the right "base" amp) but it EQs it automatically. I don't think it can apply effects other than EQ on it though. But it might be good enough for you.
I know the Axe FX does that, and Positive Grid claims that their Bias Desktop and Bias Pedal (to match distortion pedals) does it too (never tried it though).
You can find videos on the Internet of those product.
There's the Kemper Profiler that can "profile" an existing amp tone, but you'll need to have the "real" amp in order to match it. Or you can have download profiles from other users if you know which amp you want.
There is a type of EQ called a “match EQ” that can do some of what you are asking for. You play it the guitar you want to model and it stores the EQ curve of that guitar as a template, and then you play it your guitar sound, and the match EQ does some math to apply the EQ curve of the template to your guitar sound. The 2 guitar sounds can be recordings or live inputs.
It might not sound like a big deal to modify just the EQ curve, but that is a huge part of any sound. So you can get amazing results in many cases. A big part of what you like about a guitar sound you want to model is likely the EQ curve.
Another use of a match EQ is in mastering. You apply it to a whole mix to make your song have the EQ curve of another song.
There is a match EQ built into Logic Pro. There used to be a VST plugin from Steinberg but I don’t know if it still exists.
And of course if you just want to plug a guitar into a recording system with a direct box and use modeled amps, those are there in Logic Pro or Ableton Live and many other audio workstations today.
While it would be amazingly awesome, amp modeling technology has not developed far enough to replicate a given tone profile using software alone - even the high end hardware built specifically for algorithmic wave profiling won't be able to produce an exact match (thus the term "model").
The closest thing we have today is the concept of "patch" sharing, where you utilize the same amp settings, filters, eq, and other aspects of a tone that someone created by loading up the patch file to your own instance of the plug-in it was created for.