Does a filter add oscillations to a signal?
A linear filter can increase the magnitude of frequency spectra already present in a signal.  Note that the Fourier Transform of any (reasonable) waveform or signal (including ones that do not look at all like they are oscillating) will decompose it into sinusoids (which do oscillate).  Amplify any one frequency, and an oscillation may start to stand out and make it look like it just appeared; but a lower amplitude form of that spectra was already hidden in the input signal to start with.  

It wasn't added.  It was amplified.  Which is possible with an LTI filter.