OK, here's my advice.
It's very normal to feel like this after a few weeks of university when living away from home. Most people will not talk about it so you end up feeling like the only one who feels this way. Often this gets better over time, so I think your parents' idea to wait and see is best.
I guess you're committed to halls for the rest of the year? If so, then don't isolate yourself and stop going out and making friends. If you do, you will very likely have a bad time. Again, many people do not make friends instantly and mistakenly think that everyone else has got a friendship group and so they will always be left out. You don't have to go out drinking - lots of people don't like that, and you often find the drinking culture lessens after the first few weeks.
Do you have any hobbies or societies you could join? That's a good way to meet people without going out drinking.
There are lots of advantages to living in halls. It's good preparation for independent living. After all, you are going to leave home in a few years anyway. But see how you feel come the end of the year before committing to commuting (which is totally fine by the way). And in the meantime, don't shut yourself away and turn your unhappiness into a self-fulfilling prophecy.