Could antifreeze be in the engine?

Recently I had an issue where my 1996 Honda Civic temp gauge started to rise. I stopped the car to let it cool. I got to my destination and called husband to bring antifreeze to fill it back up. I drove it home that night and parked it. Found the problem was the radiator cap. Well now I am noticing when I start the engine it sounds like it struggles and the RPMs rise higher than normal. It idles fine after a moment. Could this mean antifreeze leaked into the engine?

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