First off, cool little map, it looks pretty darn good actually and the only thing I'd fix is the split river; rivers merge with others as they go downstream not split (unless there is some sort of magical phenomenon to account for it). They might split to go around something rocky to form an island but rejoin quite quickly.

As to the effects of the mountain range created by some arcane magicks...well I think the most immediate effects would be on the fauna (animals and people deserting the area for a while) while the climatalogical effects would be gradual, say over hundreds of years if not thousands.

As far as a desert forming up...that would depend on how tall the mountains are and how the jet stream blows. If it blows west to east then a desert might form up on the eastern side of the range (if the mountains are tall enough) but being so close to the coast I'm sure that there would be plenty of inland breezes to compensate for that much like the Carolinas and if this is in a sub-tropical locale then hurricanes would probably make this more like Florida. If the jet stream blows north south or south north then the mountains would have little affect the way they are now. If the jest stream blows east to west then this area would be quite swampy unless its far north, in which case it would be quite pleasant like England (which gets it's warmth mainly from the Gulf Stream but you get the idea).