the easiest technique would be to simply smell it. if it has a fruity/sweet smell, it's an ester.
chemically, you could either test for the alcohol (as you said), or test the carboxylic acid which is also produced, with sodium hydrogen carbonate, which results in co2 gas being released and the mixture turning cloudy:
NaHCO3 + CH3COOH → CH3CO2Na + H2O + CO2 (gas)
one thing with your method is that if the ester was made with a tertiary alcohol then the Potassium Dichromate wouldnt react with it, so its not foolproof
You could hydrolyse the ester with a known amount of dilute acid and then titrate. An ester would show an increase in the amount of H+ ions (but so would an amide, an acid chloride and an acid anhydride)
You could hydrolyse the ester with water and concentrated sulphuric acid catalyst. To give you your carboxyllic acid and alcohol. Then react the carb acid with a carbonate. As a carboxyllic acid is the only carbonyl compound to give off CO2 when this is done?
Alternatively you could smell it not too much though, you dont want to damage yourself