If I'm a miner, can I confirm my own Bitcoin transaction?

In theory yes, however, you would need to find a block, which is extremely rare. Miners usually participate in pools to mitigate statistical uncertainties and allow their work to be rewarded progressively. It's not because someone in your pool has found a block that your mining unit did. The operating client in your pool will probably select transactions that generates the highest possible charges. Basically, if you try to mine your transfer yourself, your transaction will probably be accepted well before you find a block anyway.

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