Giddy normally means dizzy, but it can be used for 'disorientated but excited'. When used as a character trait, it normally mean excitable, so in this case I'd say she easily gets excited by things, and probably gets 'carried away' with things. Mushy also has two meanings. The first (often used with romantic movies, couples, etc.) is romantically sentimental, 'lovey-dovey'. The other meaning (which is what this one is an example of) is to be soft and squishy. So, essentially it's saying his brain turned to mush (i.e. they stopped being able to think or reason as well as before).

2. "Mushy" means soft or squishy; easily deformable by touch. Figuratively, for a mind or brain, it means not working well; "soft in the head" is a similar usage I think. 1. Giddy is like dizzy. So, "having a sensation of whirling and a tendency to fall or stagger". Figuratively, used of a girl more than a boy, it is sometimes used to mean bright and engaging, lively and impulsive; it doesn't fit that well with "shy". It's really a neutral word; some people like a giddy person, and some don't. https://www.lexico.com/en/definition/giddy https://www.merriam-webster.com/dictionary/mushy