Welcome to TCS! This site is a great resource.
Sounds like your cat might have a URI. Given that she hasn't been spayed or vaccinated, you should take her to the vet anyways. The vet can give some antibiotics to make sure the URI doesn't get any bacterial stuff going on.
In general, URI's are somewhat common in cats, as many have feline herpes virus, and a URI is the result during a flare-up. Many cats respond well to l-lysine. It's great for helping control cold symptoms (usually flare ups of herpes virus) in many cats. You don't need to buy any special kind, although some people buy it compounded into a gel from their vet. The cats just lick the gel off your finger.
You can buy it at most grocery stores or Walgreen/CVS type stores. I buy the tablets and use a pill crusher to powderize it... then mix it into my cats' wet food. It also comes in pill form, which people break open and mix into wet food. Some people buy it already in powder form (I think this is easier to buy online).
For most adult cats, they need 500 mg a day, and sometimes 1000 mg during a flare-up; definitely check with your vet first.