When carbon dioxide is passed through limewater, you see a milky white precipitate, CaCO3(s). Lime water is saturated Ca(OH)2(aq); Ca(OH)2 is sparingly soluble in water. CaCO3, alike with most carbonates, is pretty insoluble stuff; much more so that Ca(OH)2.
Its reaction with CO2(g) may be represented:
Ca(OH)2(aq)+CO2(g)→CaCO3(s)⏐↓+H2O(l)
Note that this equation is balanced.
If you keep bubbling CO2, the white solid should go up. You should form the bicarbonate, Ca(HCO3)2, which is soluble in water, and the reaction is outside the A level syllabus. As a further tip, the best source of carbon dioxide outside of a cylinder, is carbonated water (fizzy water; water supersaturated with CO2(g)); you can cheaply pick up litres of this in a supermarket.
None of what I have written here is a substitute for doing the reaction in a laboratory
