While I completely agree with the view that some people are happy to go with the flow, not everyone is. I could not have gone on for months without sleep.
Danger - you say that he had been asleep for 90 minutes on your DH, if it was me I would have put him down in his basket or cot as soon as he had stopped feeding, especially given that this must have been at 9pm is that right?
Personally I would also aim for a main daytime sleep where he will be sleeping at night, he will then be used to sleeping there, as it is he seems to be just sleeping near you or on you etc. I appreciate this is nice and for many what they want to do, but to be honest if you want sleep quickly, or need it which is very important for your son too that you sleep well, I didn't do that.
From about 4pm keep feeding and feeding. Give him a bath at 6pm and feed some more. I have found it is very likely that they will fall asleep quite quickly if they have been fed a lot and been awake as they have had a bath etc, so I used to gently rouse them to feed some more. I always had in my head to really make sure they had a really good feed at 7pm and then put them to bed.
Then wake at 10/11pm and do the same, I actually used to wake them fully at this time, again to ensure they fed well, and did the same gently rousing them if they fell asleep quickly. Hopefully they would then last until around 3am and then you just have one night waking.
The key I always found at each feed day or night, was to try and ensure they had fed lots, if you think they have stopped encourage a bit more, and especially early evening and at 11pm.
I have said this before it is not a competition, nobody is failing, some are happy to go with the flow and not sleep well for months, but if that really doesn't work for you, then yes I think you do need a plan to guid your baby. 