1999 Honda Civic EX Overheating?

I'm going to try to explain this as efficiently as I can. My car has had a problem running hot since I got it a year and a half ago. The problem stops in the winter and comes back in the summer. This time it's much worse than usual. I have to add water to the radiator and the reservoir before every drive. There seems to be no water leaking anywhere at all, but I'm losing coolant like crazy. It makes me think there's an internal leak or that somehow the water is turning into steam within the system. I took the car to 3 different mechanics and was told 3 different things. One said there's a leak somewhere that he can't find, another said it's the water pump, and the last one said it's a blown head gasket. I don't know who to believe. I don't think it's the water pump, because there's no leak. I don't think it's a blown head gasket because there's no smoke coming from the exhaust, no milky oil, no oil in the radiator, no antifreeze on any spark plugs, and no loud engine. The same mechanic who told me it's a blown HG also told me that it wouldn't make sense to replace a HG without doing an engine swap which is another $2k that I don't have. The car has 196xxx miles on it, but the engine runs like a champ and these cars tend to last a very long time. Side note: I have replaced the thermostat, radiator cap, and cleared out air bubbles from the hoses. Anybody got any ideas of what exactly the problem might be?

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