First, I don't think you have learning disabilities. I think you just have problems with the situation you're in and maybe your grasp of the material isn't as good as it should be because there are several factors working against you.
For one thing, you should have your own separate desk. Distractions like you described take your focus off of your work more than you might realize and you should have your own separate desk and one that's strong enough to withstand the power of erasing.
Second, you should have your OWN desk. Being hip to hip to someone else is a big distraction too, and can make anyone self conscious.
Third, it might not be you so much as the teacher. When I was in school, I failed miserably at algebra. I never understood the teacher or what he was trying to explain and asking questions of him didn't help. I failed. I took it again a year later and I got straight A's the first semester. Then in the middle of the year, they took all of those who were doing well and transferred them to another teacher who wasn't as good as the first. My straight A's went down to straight D's because the teacher wasn't good at answering "why do you do it that way". She would just say that' just how it's done, which never made good logical sense to me. I've also had other teachers do the same thing to me in other subjects. I'd do poorly with them, but better when I got a teacher who could answer "why". Therefore, maybe you need a new teacher to help you grasp the problems, who can tell you why, so you can remember that every time you come across that kind of problem in the future.
You might also want to look into tutoring if changing teachers, classrooms, etc, isn't working. If you are in a college class, tutoring should be available cheap or free. You could also try different web sites that help explain why you perform certain problems a certain way. Google "homework Help" and explore the sites you find. One of them might be able to help.
For you, I think that it is not a learning disability so much as a learning difference. I have a child who understands things only if they are explained a certain way. She's 14, very smart, but if you don't know how to talk to her, she doesn't get what you're saying. She has to have help not because she's disabled, but because her brain just works differently. Even though 'normal' people can understand things given in a standard format, not everyone can be considered 'normal', even if they are highly intelligent. Einstein was, so I'm told, considered a bit of a dunce in school when he was younger, but he turned out to be one of the most intelligent people history has ever known.
Could be, your brain just works differently than the norm, but I'd bet money that you're intelligent. You just have to find the switch that turns on the light bulb in your brain where you fully grasp the lessons you're being taught. If nothing else works, talk to an adviser or someone in the department that you're having trouble with. I'm sure that they have answers that can guide you to the help you need.
Good luck.
PS: My daughter I mentioned went from straight F's to straight A's after she found help. It's just a matter of finding the right methods. You can do it too.
PSS: I say you not disabled primarily because your thought processes seem logical, you stated your question well, your spelling was good (with or without spell check, I don't know) and your writing format was reasonably constructed. I do believe you have intelligence and ability, so I'm not just being patronizing or nice. A little heavy on the ellipses, though, but that's ok. :)