Have you bought the wrong camera?
Yes.
And No.
Lets take a look at the two photos you linked to.
In order to catch water droplets there are two things you need.
1. A fast shutter speed
2. No shutter lag.
Many compacts will struggle in achieving both of these but not all and if you have the ability to increase your ISO and your camera has a largish buffer to allow you to shoot a burst of several frames than you should still be able to achieve this but it will be a bit hit & miss (it still would with a DSLR but it would be a bit easier) but then that's the great thing about digital, if you miss the shot - delete it and try again. In short, there's no reason why with some patience you cant capture shots like that with a compact camera as long as its not too basic a camera.
As for macro there are a few considerations you should keep in mind:
1. True macro begins at a magnification ratio of 1:1 not all compacts or all SLR lenses can achieve this and none exceed it without spending a not so small fortune.
2. Manual focus is often best for macro as macro often has a very shallow depth of field even at very small apertures due to the fact that the subject is so close to the camera and manual focus allows you to precisley control what elements of the subject are sharp. If your camera doesnt have manual focus capability you may want to replace it.
3. For macro photography you often need either lots of light or the ability to set a high ISO. If your camera only has a limited ISO range or its only automatic ISO than you may want to change it. A disadvantage of compact cameras is their small sensor. Small sensors produce a lot more noise at high ISO's then larger sensors which is another reason why a DSLR is really best for macro work.
4. Focal range. Compact cameras have a fixed lens meaning it has to be a bit of a Jack of all trades, macro requires close focusing distance but this is expensive to produce so typically a dedicated SLR macro lens will always focus closer than a compact camera of a similar focal length.
5. If you REALLY want to get into macro then a DSLR really is the way to go. A compact simply cannot compare in this respect but DSLR's cost a few hundred pounds and you can spend the same again on a true macro lens i.e. one that offers 1:1 magnification, not to mention then the tripod, cable release, flash gun, off camera sync cord, ring flash, reflectors etc etc

As you can see macro is an EXPENSIVE hobby so it's probably best to learn to walk before you run so stick with a compact but get one that offers macro and has the closest focusing distance you can afford at the 35mm equivalent of 100mm. If you can afford it, get one that has a remote shutter release and invest in a few reflectors or pieces of white card.
HTH