Well first- hurray for me! I had my last knee surgury in a series tuesday, and will be back on the bike in October after three years! Life has meaning again.
More importantly though, it sounds like you're describing patella tendonitis. That's an inflammation of the tendon that attaches at the bottom edge of the kneecap and the front of the shin bone. Muscles strengthen faster than tendons sometimes, and if the quad muscle is overpowering the tendon it will get overstrained and inflamed. You did say below the knee cap not underneath, right? This could be a cleat thing, but I'm thinking that a fabulous new better bike has you working harder for the fun of it, and this is a training thing. If the bike is lighter and more responsive the first thing we all do is push a bigger gear and be a bird, right?
By all means get the cleat looked at, but I think you need to back off a cog or two, and do some boring conditioning work. Spin in a middle gear and the 36 to 40 tooth chainwheel, try to think serene thoughts when people pass you, use your ankles. Pushing too big a gear too early is the big culprit in most knee troubles. A mispositioned cleat is usually pain behind the kneecap from the joint being pushed out of alighnment. Strengthening the hamstrings won't hurt either, get some leg weights and spend five minutes doing slow curls when you come in and you're still warm. Tendonitis can be a real pain in the neck to get rid off; If you can use Ibuprofen, try 400 mg 3x day for maybe two weeks. You need to have a blood level going on for it to work. Ice that puppy after you ride for a good fifteen minutes. You'll heal up, and the slower work (practice your spin!) will pay off in better total strength. Oh and taper off the dose of ibuprofen; if you quit it abrubtly it can backlash and the problem will return.
Another cool trick- and these cool tricks all come from either my orthopod or Physical Therapist- is a patella tendonitis strap, also called a jumpers strap. It's a band that goes around the leg just below the kneecap. they're made of neoprene and velcro on. There will be a rubber lump in the part that goes over the patellar tendon; this supports the tendon and helps with any overload the quad may be putting on it. These work great. I've been in rehab hell for knees lately and swear by these gizmoes. You can get one at Super Evil Wal Mart or almost any sporting goods store at the mall, $6 to $12. A little yummy smelling Ben Gay will help too.
Miss Liz