Old people in decent, or even not so decent, health, tend to still enjoy their lives. If 110 year olds have no particular desire to die, I don't think it's safe to assume that would be a common thing, especially with eternal youth and health.
Being the only immortal might suck in a way, especially if you have to keep it secret, but that's loneliness sucking, not immortality.
Likewise having to start a "new life" as part of secrecy could be annoying, but if you're regular at it then it's another chore like laundry, except a bigger and rarer deal; alternatively it might be an exciting new challenge, how to re-invent yourself this century. Either way, it's an aspect of a particular context of immortality, not immortality itself.
Living for 110 years is completely different from living for 10,000 or 1,000,000 or even 1,000,000,000 years.
Things would probs get tiring after years of dealing with it. Plus, technology advances, wouldn't someone find out sooner or later?
How would the government respond?
Immortality seems so bothersome and high maintenance, and like, life just wouldn't mean that much when you can't die? Maybe?