Final answer:
The phrase indicates Bud's sudden release of pent-up emotions that had been inaccessible, likening it to a rusty old valve that opens with difficulty and discomfort.
Step-by-step explanation:
The phrase "some rusty old valve squeaked open in me" suggests that Bud has experienced a release of pent-up emotions or a sudden access to feelings that had been closed off or inaccessible to him for some time. It's as if a part of him that was sealed, perhaps by trauma or repression, has suddenly been opened, allowing these previously stifled emotions to emerge. This metaphor of a rusty valve indicates that it may not have been a smooth or easy process, but rather one that comes with difficulty and discomfort, as indicated by the word 'squeaked' which conveys a sense of resistance and strain.