Answer: Based on your description I think it is due to insufficient light. The fragile new growth can also be related to lack of light especially if combined with excessive fertilization. Increase the amount of light the plant receives. Set it in a southern or western facing window, or better yet a room with windows on two sides. Or, consider using a supplemental plant light or even fluorescent lighting.
You can try to rinse it in the shower (although a handheld sink sprayer is easier.) Use tepid water and cover the soil with tin foil so it doesn't wash out and clog your drain. If this is just to rinse off the stickiness, I would suggest using a hand sprayer or spray bottle instead. You should be able to see aphids with the naked eye on the tips of the new growth, and spider mites would cause yellowing of the leaves and also fine webbing along the foliage and stems. If you do not see either of these, rinsing would not help stop a pest problem.
The pebbles and water would not be helpful in a cachepot as you described. The pebbles would be more effective placed in a wide flat tray (such as a cookie baking sheet) so more water surface is exposed to the air and steadily increases evaporation all around the plant.
Good luck with your plant.
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