The Doppler Effect is accounting for relative movements of source and observer at constant velocity meaning changes in frequency are sudden but remain constant.

Now can we also have source and observer moving at accellarations and frequencies changing at certain rates?

Yes, just like you expect it.

Just remember that the frequency is only changing relative to the observer, so you can use the normal doppler effect equations even for an accelerating body, just plug in the instantaneous velocity of the observer at the moment he is measuring the frequency and the original frequency that was emmitted by the source and that will tell you what the accelerating observer sees.