Until it has healed, anything that rubs against it will rub it raw and hurt him. Imagine you've got new shoes that have rubbed your heels raw - it takes a while before it's not sore doesn't it? The skin in the girth area is quite soft and delicate, unlike our well-trodden feet - so however soft a fleece girth cover is, it's still going to cause friction on a raw patch.
Best wait for it to heal, then use the girth with the Fleece cover.
Get up, get going, seize the day. Enjoy the sunshine, the rain, cloudy days, snowstorms, and thunder. Getting on your horse is always worth the effort.