i dont know much about skimmers on small tanks (i dont even run one on my 40 right now actually...mostly cuz mine doesnt work tho lol) But usually a 12 gallon tank probably wont need one as long as you keep up on water changes. So do you?
Also, what type of water are you using? If it is tap water, it probably has nitrates in it, so even doing a water change or topping off wont help...you'l just add them right back.
Do you have any chaeto or other stuff in a fuge? That definately helps.
Lastly and most importantly imo, are you running any bioballs or any other filter media (bioballs, biowheels, biomax or other ceramic medias)? If so, those all make nitrates, so if you have them, slowly take it away and add live rock if you dont have any right now.