OP your DS sounds similar to DS1 he can't write, to say his hand writing, what there is of it is illegible is not doing it justice, and it's very slow he averaged 3 words a minute. He was assessed at 8 and diagnosed with "dyslexia " although the ed psych who assessed him who I later found out is considered to be one of the worlds experts in dyslexia said some would dispute this diagnosis because he can read very well and has excellent comprehension and spelling is pretty average.
My DS like yours is different from his peers, a very fussy eater up until a few years ago (he's 20 now) especially when he was younger, he's popular with other and exceptionally empathetic and very caring and considerate, he can almost mind read but he is also very affected by others moods, e.g. even slightly teachers irritated upset and worry him very badly. He is hypersensitive to certain noises particularly related to clicking noises e.g. heals walking down a corridor, he has to look up at step as he is unable to filter it out (we only found this out when he was in his teens and he could tell us), He also has a photographic memory, he can quote sentences from books he read 5 years ago and can remember huge chunks data if it's something that interests him he is also exceptionally articulate. His initial ed psych report scored his IQ at 132 but his processing was in the bottom 3% and working memory bottom 10%, this was of great interest to the ed psych because this level of discrepancy between intelligence and processing is apparently "very rare". He has recently been reassessed for university, (yes he made to university no where amazing in terms of entry requirement but he got in just and he's very happy) another fascinated ed psych, who spent 30 minutes after the assessment telling me how unique he is, he now scores 147 for IQ, reading comprehension etc are in line with his ability, maths crap, processing no change working memory slightly worse.
The bad news is if your DS is anything like mine he will struggle to access and achieve in education in either sector. My head aches from banging it against a wall of couldn't care less teachers. He's attended eight schools between 2 and 18 in both sectors and only 1-2 teachers actually understood him most wrote him off. All excepted he was very bright but none wanted to help him. You will have to fight tooth and nail to get any kind of useful help and even then he got very little.
I completely disagree with reallytired get your DS assessed now he's definitely old enough, if he has signifucant issues he needs at the very least to use a lap top, the sooner he does the quicker he'll learn to type and it will then be off use in exams etc if his problem is really bad in the ideal world a speech recognition programme like Dragon, good luck with that one.
I was told many years ago that my DS cannot be changed, basically amongst other things he cannot process information onto paper by hand, it doesn't mater what you do: practice, encourage, bribe intimidate he will not really be that much different this is the way his brain is wired up. You wouldn't insist a one legged man run a marathon but you can enable a one legged man to run a marathon with an appropriate prosthesis. I was also told if he were to make a significant improvement in his writing/processing etc it will have a detrimental affect on the things that he is good at, his brain has compensated for one defect by over developing others, this is the person he is. Issues around his his mental health were was highlighted as a potential problem when he was 8. The best anallergy I ever heard was Porsche, engine lawn mower gear box and that life for him must be very frustrating and demoralising.
Good luck to you and your DS if he's anything like mine trust me your going to need it.