Neurontin can causes drowsiness, dizziness and unsteadiness of gait. The product information states that a person taking this medication should not drive or operate machinery unless they are sure they are not experiencing these side-effects.
Morphine, as has been said, can cause drowsiness, depression of respiration and impairment of judgement. However, people become used to the effects of morphine very quickly, so it is possible to be taking quite large doses and feel entirely normal.
From what you say, you are not experiencing any significant side effects topside. However this does not necessarily mean that you are not going to experience them at depth.
I think it is highly unlikely that you would find a doctor who is prepared to certify you as fit to dive while taking these medications.
Similarly, I think it is unlikely that you would find a dive operator who would be prepared to let you dive while taking them.
So the options are either not to dive, or to conceal the fact that you are taking these medications, and to take things extremely cautiously. If you are an extremely experienced diver and making these dives means the world to you, you might consider taking the chance. However, I gather from your post that you gained your certification not all that long ago and may not have a great number of dives under your belt.
All things considered, I would advise strongly against diving.
Remember, you would not just be putting yourself at risk. There's also your buddy to consider. What's more, if anything went wrong, you could be creating a world of hurt for the dive operator.
Sorry Justarius, but that's the way I see it, and that's how I would advise you if I were your diving doc.