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Hi @Dimebag first… Great name. Dimebag Darrell was a terrific guitarist!
Forgive me if you already know and have done so… But getting a proper setup on your guitar can help with this. Think of your finger as a beach ball and the strings as a couple sticks. If you put the sticks on the ground you can get them close to each other without touching the beach ball… If you lift the sticks too high, then they touch it .. that is kind of like the string action with your fingertips.
As far as using the sides of your fingers… I’m no expert but that doesn’t sound like a good long term solution. If it is still a problem with a well setup guitar, you could consider a classical or flaminco guitar. They have significantly wider string spacing. Willy Nelson uses a beat up old classical guitar and it sounds amazing.