I would advise heavily against using non-steroidal anti-inflammatory drugs (NSAIDS) to treat any form of anxiety or depression or what have you. It's simply not what they are made or used for. As I'm sure you know, they are used to treat mild pain and in a general sense, are not good for your liver. The only reason that anyone should be on a long-term regimen of NSAID's is with a medical professional's (preferably a real MD who is familiar with your medical history and can confirm that your hepatic system can handle the added stress without provoking toxicity) advisement. In short, please get this particular idea out of your head for your own good.
Now, for the Dextromethorphan (DXM) which if am correct is the dextroratory isomer of the opioid drug "racemorphan", not in medical use in the USA. The opposite side or "isomer" of this drug is apparently where the drug gets it's opioid effects. DXM is a dissociative drug often compared to drugs like ketamine, pcp and analogs thereof. If taken in high doses it will cause the above mentioned effects. In my experience, it was distortion of vision, slowed reaction, sound, a feeling of floating while walking, feeling like everyone is talking to me (you lose your ability to comprehend voices and identify who is conversing with who).
I really don't think that DXM should be used as an anxiolytic or antidepressant. If it were to be used for this purpose, the dose would have to be carefully controlled, which is quite hard, especially for someone with any kind of mental anguish. The urge to take "a little more" can be quite strong.
