Can you mine your own transactions yourself?
Theoretically, if you can mine blocks then you can certainly include your own transactions in the block.

Practically, you are competing with every other miner on the planet to find the next block. If you "win", you get the block reward plus you get to choose which transactions are included in your block. If somebody else wins, you get no say in the matter. Unless you have a very large mining operation, the chance of you winning is so small that it's never going to happen.

Miners who do make new blocks today (somebody has to, after all) may choose to include their own transactions in their blocks.