Getting bitcoin transaction fees is the same as mining a bitcoin block (and getting the block reward). My understanding is that you think it's possible to just mine transactions on their own and get the fees, without participating in the very hard job of creating blocks. However, this is not possible.
Because transactions are verified by miners putting them into blocks, there is no way you can verify transactions (and therefore get the fees) without creating a block.
Since the total combined hashrate of the bitcoin network is so large and takes ~10 minutes to create a single block, your machine on its own would probably take several millenia before ever finding a block (and thus getting transaction fees from the transactions you place in the block + the 12.5 BTC block reward). This is why pools exist in the first place, because no one has enough hashpower to find blocks on their own (except a few huge miners) and the only way to mine BTC is to create blocks.