I don’t have a solution to offer you, but this is a common things being experienced by a lot of guilds on realms that are effected by the realm connections. None of us can see our guild applications and have had to make due by inviting manually. For a temporary fix, I would have another guild member invite your alt while you’re on it via the “/ginvite” command.
Some users in another thread have offered some fixes, but I personally haven’t had any luck!