You raise two good points about oxygen therapy that need to be explained.

An increase in the frequency of attacks after starting oxygen therapy is very common and strangely enough, a good sign the oxygen therapy is working effectively.

Here's why: 
1.  You are likely achieving aborts with oxygen therapy at lower pain levels but the time to abort at the higher pain levels are taking much longer. What we've found over the last few years while a flow rate of 12 to 15 liters/minute may be effective for low level hits at pain level 5 and below, flow rates this low will not be effective due to longer abort times greater than 20 minutes for attacks at and above pain level 6.   This basically proves the fact that there is a direct relationship between time to abort with oxygen therapy and increased pain levels.  In short, the higher the pain level after starting oxygen therapy, the longer it will take to abort the attack.

2.  Flow rates that support hyperventilation have also proven to be more effective up to pain level 9 with shorter abort times ~ an average of 7 minutes.

3.  Aborts with oxygen therapy at flow rates that support hyperventilation are frequently so short they abort the pain of the cluster headache but not the cluster headache triggering mechanism.  When the effects of oxygen therapy at flow rates that support hyperventilation dissipate and the triggering mechanism is still present, the attack resumes...  this frequently takes 15 to 45 minutes.  We call these attacks "Re-Attacks" rather than "rebound headaches" as a rebound headache signals a built up resistance to a headache medication...  and if you had a resistance to oxygen, you would have assumed room temperature a long time ago and would not be here to post.

4.  The frequency of re-attacks tends to start dissipating during the 3rd to 4th week after starting oxygen therapy and are completely gone or significantly reduced by week 8.

5.  The incidence of re-Attacks can be reduced significantly by staying on 100% oxygen long enough after the abort to bring the total exposure time up to 15 minutes.  You do this by aborting your attacks at the higher flow rates that support hyperventilation and as soon as the pain is completely gone, reduce the flow rate to support a normal respiration rate for as long as it takes to bring the total time on oxygen up to 15 minutes.

An increase in the time to abort is a different problem.  We are not sure just why this happens, but it appears the longer abort times are due to a decrease in blood pH (too much acid). When this happens, the triggering mechanism becomes more effective as a low pH causes more cerebral vascular dilation making the attacks more painful.  The low pH also makes abort with oxygen therapy or any other abortive take much longer.

One of the things I do when this happens that tends to help is to take calcium citrate with vitamin D, magnesium, and zinc tablets (3 to 4) prior to the evening meal.  These tablets act as a buffer to bring blood pH back to neutral.  If you don't have any of these on hand, Tums are a good source of calcium in a pinch.

Hope this helps.

Take care,

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