MC34063A - 3.7 to 1.5 buck converter voltage rises when load applies
Your inductor is probably too wimpy, and is saturating.  Do a simulation of your circuit, or scrutinize the MC34063 data sheet for the peak and RMS current expected in the inductor, then select an inductor that exceeds those values.  Or better yet, simulate the circuit.

And your cap looks like an ordinary ol' electrolytic, so it probably has a fairly high ESR for the task.  If you know the ripple current then you can calculate the ripple voltage just from the cap's ESR -- a good starting place is probably to assume that the current is 500mA peak-peak (i.e., that the supply is just at the border between continuous and discontinuous).  I absolutely cannot remember what the typical MC34063 circuit does, so you want to consult the data sheet there, too.

Get through those, come back with your updated circuit, and we'll start talking layout.