Galvan is terrified of Morbols mainly because of how many Bad Breaths he had to endure as an adventurer. One of which landed him bedridden for a week.
He hates being cooped up indoors too, especially when sick or injured. He's always been more fond of the outdoors and hates the feeling of being confined in a small space for long periods of time. If he's sick or injured and has to take 'bed rest' he will, naturally ignore it and try to get outside. One time at the Crystarium he jumped out of the balcony after being stricken with a cold (it didn't work and Y'Shtola had to have someone watching him after that incident) and in a less humorous one, a few days after waking up after his fight with Zenos, Galvan did attempt to leave Ishgard but could only manage a few steps past his bed before collapsing.
His claustrophobia only worsened after the fights against Titan and the infamous landslides that 'killed' him