Will the burn subside?

Is the burn in the muscle (back of leg/calf) or the bone (front of leg/shin)???

I cannot speak to your pain, but when I started running in January at 250 ( I now bounce between 235-240) I had more aches and pains from the knees down than I had words to describe them.

It took a consistent, slow-but-steady two months (and 1 good switch in running shoes) before they went away.

The first 4 weeks were run/walk combo's.

I just focused on bike and swim for cardio, and running to get used to miles while avoiding injury.

When I started running, I had similar pain (plus other parts of the body thanks to the 255lbs I was carrying).  But seriously, simple things that helped me was making sure I had good shoes, new ones, that fit me and were for my running style.  I also learned that tying my shoes too tight caused pain in my ankles and shins when my feet started to naturally swell while running. 

The pain is mostly in the back and starts to wrap to the front.  I believe it is muscle pain.  I do wear running shoes and was fitted for them at a running shop and they have i-bungee laces.  I am sure it is probably conditioning that needs to take place since I just started...I am looking for a glimmer of hope that the pain doesn't last forever, everytime I run.

I had this problem, its due to weak calf muscles, try doing 3x10 standing calf raises off of a step or calf machine if you goto a gym on your non running days, and stretch the heck out of your calves, like 10-15 minutes of good solid stretching before and after your runs.  It will take some weeks, but the pain will start to go away because your calves are stronger. 

if its REAAALLLLY bothering you, go talk to you doctor. i am not one but have been running forever and will give my non-medical thoughts.

my instincts at first says shin splints, but you say its in the muscle (back meaty part) and not between the two lower leg bones or on the front bony part. it sounds like you are saying its in the tendon that connects your calf and ankle, which makes me think you are pushing off hard on the balls of your feet.

three suggestions that might help

1) have you tried running/ walking on grass or trails? this may make for a softer landing.
2) are you running/ walking more on the ball of your foot? sometimes my calfs hurt when i do speed workouts (sprinting) because I am running on the balls of my feet. try not to run on the ball of your foot but land on the heel and allow the foot to roll forward and push off on the ball of the foot (its natural motion).
3) jog/walk for a warm-up first that is very light and easy to get the body/ muscle temp up (i run 3-4 mins at +10min/ mi pace, stretch, then do my full run at 9min/ mi pace) before you stretch. i have read studies (both for and against stretching before/ during workouts) that streching cold muscles may make it easier to damage them during a run.

lower leg injuries start small but can lead to stress fractures or other things so its really not something to take lightly.

forgot to add that if you are on a hilly area you will spend more time on the balls of your feet and you will feel it in your calfs as well.