Love letters should work...
"Love letters" are private messaging between the players and the GM in the form of written slips of paper passed between the communicating parties. To overcome the obvious drawback that passing messages in writing between yourself and the GM is highly conspicuous and will likely cause your secret to be revealed, ask the GM to have all players pass a love letter, not just you - eg. by saying "okay, the person who has a secret, write your secret on this slip - for the others, write your character's name". You can agree a secret signal with the GM to cause the slip prompt, eg. a subtle nudge under the table. By my experience, love letters do their job but are a bit cumbersome, can cause an undue distraction and will of course reveal that at least one party member has a secret.
...as should modern instant messaging...
You and your GM can use an instant messaging app or SMS to pass secrets. This overcomes some of the difficulty of love letters but requires that both you and the GM use your phone, which is often a faux pas at game tables. The main advantage is that the fact that one of the players is doing secret messaging with the GM doesn't have to be revealed. We've used this system in some of our games to much success, although we don't use it much anymore because of what I'm saying in the next part.
...but I can't really recommend either.
As a frame challenge, my personal experience with player-level secret keeping is that it's not really a good fit for games that don't specifically revolve around the concept, and that asking players not to meta-game is often a far better way to get them not to meta-game than trying to prevent it. I don't know your players, but most players I've met respond to in-game ways of preventing them from gaining information they want with off-game reasoning, which is exactly the kind of meta-gaming that worries you. If you try to hide it from them, they're likely to believe you're trying to trick them, and can hardly be blamed for trying to sort the situation out.
Contrarily, being open about your character's secret can encourage the atmosphere of trust between you and the other players and make it clear that your character's secret agenda doesn't mean you're trying to fool them in any way. With such an atmosphere, you can be open about your character's secret and the other players are not likely to meta-game to expose you - they don't have a reason if they don't believe you (the player) are hiding something from them.