When we say "... but it's a nice problem to have", what we're often doing is indicating that we're complaining in order to vent frustration or anxiety we're fee

When we say "... but it's a nice problem to have", what we're often doing is indicating that we're complaining in order to vent frustration or anxiety we're feeling, and that the person we're talking to isn't expected to take any action other than offering sympathy. Translate it as "this sucks, but I'll be fine".