The delayed onset soreness that is related to HEAVY lifting if due to actual micro trauma to your individual muscle fibers. The heavy lifting actually tears your muscles down at the individual fiber level (what you want) and then your body rebuilds the tissue but adds more tissue so that the cross sectional area is increased which causes absolute strength gains. The delayed onset muscle soreness is usually worse after the first two days, most atheltes say the second day is the worst and it diminished from there. 8 to 10 days seems extreme and combined with the joint issues you discussed my intuition tells me that you either did not do a periodized strength training program that had a anatomical adaptation period (training to train, gets your connective tissue, joints, etc. ready for real lifting) and then a transition period (an in between period where you increase the loads and decrease the reps to get ready for the heavy period). There is an article I wrote on the VT site that is titles Periodization in Strength Training
that goes over all that. Having the training periods that precede a heavy period not only drastically increases the strength gains that a heavy period of lifting can provide but it also much safer as your tissues have enough strenght to carry the heavy loads.
There are also immediate actions you can take to minimize or shorten the period of extreme muscle soreness. First off, stay very well hydrated. Next is to do very easy aerobic exercise the day of and the days after. This is very easy aerobic work like cycling and it doesn't have to be long, say 30 minutes. The light exercise will increase the local muscles' metabolic rate which in turn increases the rate of healing and tissue building. Lastly is to eat correclty: you need to replensish both carbohydrates (the gas in the tank) and the proteins (the building blocks). Recovery drinks in the 30 minute time window right after exercise can help but you also need to eat correclty otherwise.
The soreness you feel right after doing a set, or the "burn" is caused by a local rise in lactic acid but contrary to popular belief, your body dissipates this rather quickly and lactic acid is NOT related to delayed onset muscle soreness.
I hope this helps and keep up the hard work but be smart about it!