I can see some sort of insect on your plant, small tan coloured objects which may be citrus scale. Scale produces honeydew, which is likely what the sticky fluid droplets are; this often leads to the secondary condition, Sooty Mould, though that is more likely outdoors than in. Check the whole plant, including backs of leaves, stems and woody parts, to confirm, and then treat for the problem. If you can get neem oil spray where you are, that should do it, though you may need to repeat the treatment more than once. Even if you decide it's not scale but some other infestation, neem oil should treat for it, but the commonest infestations in these plants are mealybug, scale and aphids. More info in the link below - it's a blogspot, but does contain a useful photograph of brown soft scale, and information as to how to deal with it, you'll need to scroll down a bit, it's not at the top of the page
http://thecitrusguy.blogspot.co.uk/2010/03/lets-tip-scale.html
It's probably worth checking your other plants from top to bottom as well, to make sure they haven't acquired an early infestation of the same problem. If you cannot find a suitable oil spray, you will need to check for insecticides which say they will deal with this problem - but if you're expecting to eat any fruit produced by your plant, you must choose a treatment which is safe to for use on edible plants.