it appears to be coming underneath the block that is above the concrete slab that is the floor to the room behind the planter.
OK. Generally speaking, all houses should have a foundation level which may or may not be damp depending on the condition of the ground it stands on, and a level above the foundations which is part of the house structure and which should not be damp. Between the two layers there should be a form of waterproofing, which I know as a "damp proof course" which stops damp from foundations from wicking up into the house. The damp proof course should be above ground level, so that damp from the ground can't wick into the house through the walls from damp ground above the damp proof course.
Usually this damp proof course will be at one single level all around the structure, and should be obvious once you start looking, but when there have been alterations it can be at different levels and that can cause problems. (I'm assuming no basement here, which is a complication I've never had to deal with.) I'm hoping here for your sake that the concrete pad which used to be the carport has a waterproof layer of some sort to prevent damp from coming up from underneath, and even better if it was part of the original construction. But as a car port, there would not have been walls. So the new walls may have been built without a dampproof layer. If they were built on top of a concrete pad which did have a dampproof layer that's not a problem. If they were built straight onto the ground, or on a concrete pad which could itself become damp then that is a problem. From what you say, the damp is coming in at or above the level of the pad, so I think you are basically all right, with walls built on top of a waterproof pad.
That means that your big question is: how are the relative levels between inside and outside? I'm seeing 9 courses of brick below the window sill and above the tarmac, but the tarmac appears to be covering at least one more level of brick. So how does the level of tarmac outside relate to the level of the concrete pad/level of the damp proof course for the rest of the house? It looks to me as though the problem is that there is damp ground outside which is wicking damp through the wall/bottom of the wall.
There will be a way for damp to get in as long as there is material against the outside wall which is above the level of the damp proof course/level of waterproofing in the concrete pad. The permanent solution is to dig out the tarmac against the wall down to the below the level of the waterproofing, so that there is no damp material against the wall at all. If that leaves a deep trench against the wall that you can't live with then the answer is a dutch drain/french drain as suggested by CCCA.
Waterproof paint (only once the wall has dried out, otherwise you are just sealing the damp in) may only be a temporary solution, if there is still a way for damp to get into or under the wall because the ground level outside is too high relative to the damp proofing.