Lower leg pain is not unusual in new runners and has several causes. Knowing details about your running, when you started, how you've progressed, and your routine would help in figuring out what is going on.
- shin splints: Basically soreness caused by overuse of the shin muscles. This usually starts 1/2 mile to a mile into a run and does not usually involve ankle and calf. Except if the shins are really bad, other parts of the lower leg may be over-stressed as a result. Stop running for a couple weeks, do exercises to strengthen the shins and lower legs, then resume at lower intensity (speed) and shorter distances. It is possible this is what's going on, though you may be past this point and into stress fracture. The compression sleeves offer some support, but probably not enough to matter. That much ibuprofen is likely a bad idea, since it can have other effects (bleeding) that may be making the problem worse. Ice the first few hours after running, rather than ibuprofen. And none before the run.
- stress fracture: Micro-fractures of the bones, again due to overuse and stress that the bones aren't up to dealing with. Pain can start immediately on exercise and will often continue during daily life. Sometimes result from untreated shin splints. Can be diagnosed by MRI or bone scan. If the fractures are old enough (several weeks), an x-ray may show new bone forming as part of the healing process. This means a visit to the doctor. And no running for 6 to 8 weeks (minimum), followed by a gradual resumption of running. It's possible this is where you're at, based on your symptoms, though it is uncommon in both legs at the same time.. If left untreated can result in a full, actual fracture.
- compartment syndrome: "Compartments" in the muscles develop pressure as you run and normally expand some to accomodate the increase. In compartment syndrome, they don't expand, causing pain. This usually starts when you start exercising and stops when you stop and the pressure subsides. There are non-surgical treatments - google "compartment syndrome". Surgical treatments involve cuttting the fascia around the muscles to allow the pressure to be relieved. I had a friend who had the surgery and it was a long and rocky road.
Good luck.