I think JB might be onto something there. Since finding myself a ligament down a few years ago I am way more cautious on heel hooks, and also have the same kind of 'afterglow' following some problems.
Some things that have helped me:
a) Caution - as you outlined in your OP, just being careful to avoid repeated aggressive moves
b) Working on hip mobility
c) Maintaining good strength and flexibility in quads, hams, glutes and all of the muscles around the groin/pelvis
Your knee is basically just a hinge; all of the twisting/rotation needs to come from your hip (or ankle), so I try googling 'hip mobility' or visiting MobilityWOD and checking out the hip mobilisations. I've found that even just warm up drills to increase the range of movement in a side-lunge or 'knees out' squat position are really helpful.
I don't think clicky knees are a problem intrinsically, but they can sometimes indicate damage or debris. Unless you get pain/discomfort I wouldn't worry about this. Squats are a good idea mainly because they improve your hip mobility in a practical way; look up 'goblet squats' and do a few sets every day until you can manage deep squats with wide knees.
In terms of strength, doing some goblet squats with a dumbell or kettlebell, and some deadlifts or romanian deadlifts with a moderate weight will go a long way to increasing the stability of your knees. Personally I have found that doing 'rear foot elevated' squats (sort of a static lunge with the back foot up on a bench) really useful; working up to 2x30kg dumbells for several short sets. Even unweights it's a great exercise that you can do in the park. I would warn though that you need to really focus on form and make sure that your front knee doesn't come more than an inch or so forward of the toes; really sit back and down. Loads of vids on the web.
Basically anything that requires you to stabilise and drive your upper leg using your glutes and deep supporting muscles is likely to help.
EDIT: Oh, and meant to say remember to keep working on your hamstring flexibility. Not normally an issue for climbers but worth checking. Tight hamstrings mean quite a bit of strain in the knee when you have to raise your leg up high. If they're flexible, you will start a heel hook from a less compromised position.
