I meditate daily for 30 minutes, and right after each session my mind is very calm, centered, stable; I just exist in the present moment without much thinking. However, after a while, the compulsive thinking comes back, wants to drag me towards unhappiness. I feel this is like an illness. Therefore, is meditation a cure to this illness (will it go away one day if I meditate more/longer? What should I do?) or is it just a temporary easing of symptoms? I want to cure the illness. Thanks.
That depends on the type of meditation you do. To most people, meditation is all about focusing the mind on one thing and enjoying the bliss that comes with it. This type of meditation is called Samatha(tranquility) meditation. There are many forms of Samatha meditation. Ex: breath meditation, loving kindness meditation, repeatedly chanting a word etc.
Samatha meditation is taught in Buddhism too, but the meditation type that is unique to Buddhism is Vipassana(insight) meditation. Samatha meditation is mostly about fighting off the symptoms and looking for a temporary relief. Vipassana meditation is about curing the sickness that causes the symptoms. Here's a handbook on how to practice Vipassana.
To think means to divide!
Stopping thinking does not stop suffering!
Have you ever tried to listen to your thoughts? The mind itself is trying to tell you something. Listen! The fact itself that you can only meditate for 30 min is its a sign that you don't have inner peace.
Dzogchen Practice in Everyday Life by HH Dilgo Khyentse Rinpoche:
We should realise openness as the playground of our emotions and relate to people without artificiality, manipulation or strategy.
We should experience everything totally, never withdrawing into ourselves as a marmot hides in its hole. This practice releases tremendous energy which is usually constricted by the process of maintaining fixed reference points. [more ...]
Now learn true meditation and don't stop a minute!