Question: I am in need of some help with a project. I am trying to build a circuit that will turn on three LEDs randomly on a 1-5second cycle. I have the basic when it comes to electronics, but get stuck on the random part. I have started with a 555.

Answer: 
Yes, Hall effect sensors sense the magnetic field caused by current, and can therefore measure absolute current. A current transformer can only sense current down to some minimum frequency below which gain falls off rapidly. A current transformer can't sense a fixed current.

If you are measuring current of something that is inherently AC, like the power line, then a current transformer can be appropriate. If you really need to sense DC current, then you can't use a current transformer and a Hall effect sensor may be appropriate. Keep in mind that a Hall sensor requires separate power to operate.

The other major way to sense current is by using a sense resistor. The resulting voltage is not isolated, so that may need to be dealt with. In the case of a sense resistor, it is often convenient to put some detection and processing circuitry together with the sensor. That can the convert the result to digital and send the digital information over some isolation barrier, like a opto-coupler.
There is a way to detect DC current with a transformer - It is called a flux gate or zero flux DC current transformer. The technique was written about in 1901 in an IEEE paper, was realized in an HP 428B milliammeter from the 1950s or 1960s and used in other applications today.
Essentially, toroidal cores with equal and opposite windings are excited by a sinusoidal waveform. This produces zero net flux in a winding common to both cores - the cores should be matched orthogonal cores. If a DC current flows in a wire through the center of the cores, it produces a net flux as it subtracts from one of the cores flux (the other core is saturated further). The common winding then indicates a net flux which can be bucked with a second common winding current which is proportional to the net flux/current in the sense winding. A control loop is used to close the loop and drive the net flux to zero. Pretty cool stuff. I am surprised it is not used more often and suspect it is easier/cheaper to use hall effect sensors.