My wall appears to be leaking. Can I fix it myself?
Unless the source of the leak is a pipe, the issue will be to the exterior of the house. Could be a leak darn near anywhere on the exterior as water will travel, but in this case, I would hazard a guess that the window is leaking or there is a valley that is cracked near that window.

As far as a hiring a professional goes, that is entirely dependent on your level of comfort of getting in that area of the exterior and checking for damaged areas.