[Question] I have deformed thumbs and I must play guitar

Okay, maybe not deformed, but I have toe thumbs (or club thumbs, or Irish thumbs, or murderer's thumbs, or those weird thumbs that Megan Fox has, depending on who you ask) and they're significantly shorter and broader than most normal thumbs.

I/m also a v small girl and have short fingers to begin with. I'm in a loud aggressive punk band and still learning so my strumming is a bit messy and often I end up hitting the E/A strings when I don't want to. Our other guitarist keeps saying 'just use your thumb to mute those strings!' which I understand in theory but in practice.... does not work.

Does anyone have any alternative suggestions for how to eliminate this problem without getting like, finger extension surgery?