Lexapro is an SSRI, and SSRIs usually take around 2-3 weeks to begin really working, as the medicine has to have time to build up in the bloodstream. Because of this, what you felt just might have been somewhat of a placebo effect. (I've been taking Lexapro for almost 5 years and I experienced the same thing when I began taking it).
The National Alliance on Medical Illness states that "Sleep, energy, or appetite may show some improvement within the first 1-2 weeks. Improvement in these physical symptoms can be an important early signal that the medication is working. Depressed mood and lack of interest in activities may need up to 6-8 weeks to fully improve." (link: http://www.nami.org/Template.cfm?Section=About_Medications&Template=/TaggedPage/TaggedPageDisplay.cfm&TPLID=51&ContentID=66272
If I were you, I'd just give it a couple more weeks to see how it goes, especially because you're not really having any major side effects, which is a really good sign. In terms of increasing the dosage, I can tell you that I started on 10 mg and now take 30 mg alternating with 40 mg and never had any issues with increased side effects. Lexapro is tolerated pretty well as far as SSRIs go, so I wouldn't worry if I were you. As long as you're not experiencing any bad side effects and are okay taking the medicine, there shouldn't be a problem. And even if you were to get some bad side effects, you can just stop taking the medicine and you'll be fine!
Especially because you are
feeling better in terms of your anxiety, you should definitely give the medicine a little more time to start working. When you see your doctor next, he/she will probably ask about dosage increases and you can discuss that then. I hope this helps! :)