Okay you will have to clean a 3l daily until you can get your hands on a larger tank. I recommend 5g, here is an awesome one for a cheap price. It has everything you need: http://www.tropicalfishkeeping.com/b...82/#post296909
Your betta is freaking out because he has no furniture. We are talking about a fish who lives in flooded fields... They don't take too well to a bare 3l tank. In fact, not many fish will... every animal needs a hidey-hole to call their own-- unless they are a jellyfish lol! What you are seeing is a fish trying to hide... in a tank with no hiding spots! No wonder he is freaking out! When you are picking up a decent tank, be sure to swing by a hardware store / craft store / walmart etc and pick up a big cheap pack of silk plants. Your motif: jungle. There is no such thing as too many plants lol.
Hope that helps!
You can read here for more ideas on how to give your betta a decent home... they will live for anywhere from 3-7 years if all their needs are met: http://www.tropicalfishkeeping.com/b...are-faq-20058/
Welcome to the forum!!!
EDIT: I also suggest you keep the betta in a dark room until you can get him some shelter... fish can (and do) die of stress and we need to get him to stop swimming lol! Also make sure the top is covered; bettas will instinctively try to jump over to the 'next puddle' if they find themselves trapped in a small space.