I get these cramps in my fingers whenever I play songs that use the chords Am, F and C

and I'm thinking it's because they have a similar shape (I do F this way: https://www.drbanjo.com/chords/f_chord_plain.png)

and I'm thinking if anyone knows how I can get rid of it, because it really is killing me sometimes and a lot of the time I have to stop the song or skip a few chords x_x

the strength in my hand is pretty good and I stretch before playing.
My hands cramp up too, but part of that can be chalked up to me being an ol' coot with arthritic tendencies.

Found this basic article to be a good launching point for limbering/stretching before practice or playing.

I am a StarGeezer: some call me..."Tim."*

* - Heartfelt apologies to Monty Python for blatant plagiarism. Those responsible have been sacked.

Epiphone G-400 "Goth"
Peavey Vypyr 75 Amp
Quote by Tony Done
Are your hands warm enough? I occasionally used to get cramps from cold hands, I still get cramps from cold feet in bed.

yep my hands are warm, I know what you mean lol my feet get cold a lot too.
Try warming up by playing some other stuff first, then play those chord progressions until you start to get a cramp, play something else for a while, then try them again. That's about the only advice I've got.

And of course use only as much finger pressure as necessary.

You could always change the way you play that F chord to more of a barre type thing with your index finger covering the first four strings too. Then once the cramp goes away go back to the original way.
G'day, mate,

Just looking at that photo, I think I might see why you're cramping. Now, keep in mind I've never had a lesson, but I am at one with The Force, and I'm pretty sure it's because you're straining your tendons in your pinky (smallest finger), so try a modified version of the above advice, perhaps, and try either relaxing that finger, or let it rise above the fret board?

I just had a look at mine, playing F Am and C and the pinky hovers over the strings, waiting to jump into a 6th or 7th, if that helps?

Just repeating, though, I don't have the faintest idea what I'm talking about when it comes to technique; I am only addressing the physiology of what you're doing.

Hope this helps.
To name a thing, is to pay it respect.
Try to use substitute C9 for Cmaj, Fmaj7 for F and Am7 for Am. It will still sound the same. It will prevent you from having occasional cramps while playing.