This is a classic case of apophenia - when your brain detects a pattern in random events. Times like 11:11 or 22:22 look unusual precisely because they're symmetrical, so your brain spots and remembers them more easily. When you look at a clock dozens of times a day, the odds of catching at least a few of these "pretty" times are pretty high. If you were catching, say, 14:37 or 09:43, you simply wouldn't pay attention - and you're missing coincidences like that every single day.
A sign only works if you believe in it, meaning you're unconsciously waiting for that coincidence and getting excited when it happens. It's basically self-suggestion: you're already primed to search, so you find. Friends talk about "universal communication" because those stories are interesting - it's way easier to believe in a sign than to think about probability.
If it's bothering or distracting you, just stop deliberately checking the clock looking for patterns. If you notice it by chance - just enjoy the cool coincidence and move on. There's no magic to it, but there's no harm in pleasant coincidences either.