Not quite, mate. Having a digital signature doesn't mean you have the private key.
The private key is used to create the digital signature, but you can't work backwards from a signature to get the private key. That's what makes it secure!
So even if someone sees your digital signatures (which are public), they can't figure out what your private key is. It’s like how someone might see your handwritten signature on a document, but that doesn’t mean they can forge it perfectly.
Always remember: keep that private key safe!