Jimmy telling Chuck he's a lawyer and Chuck getting "sick"

In 1992, Chuck visited Jimmy in jail, where he bailed him out, in exchange for Jimmy turning his life around. During the subsequent nine years, Jimmy turned his life around to a degree and passed the bar exam. In 2001, Chuck stopped coming to the office, due to his developed electromagnetic hypersensitivity. By this time, Chuck's marriage with Rebecca has fallen apart.

Currently, one episode into Season 3, the nature of Chuck's electromagnetic hypersensitivity development has yet to be revealed. However, judging by the elliptical flashback style of the characters' back stories, it can be speculated to be a poignant plot point that will further explain the brothers' complicated relationship.

Minor spoilers up to S3E5! (but I think OP's question implies he has seen this episode).

Was Chuck's illness based on a necessity to occupy Jimmy's time, and keep him from practicing law?

Chuck seems to believe in the existence of his own disease. He has taken measures that do not impact Jimmy's ability to practice law directly. And he has inconvenienced other people even if it was completely unrelated to Jimmy.

Chuck is a master manipulator, though. He exacerbated his condition in order to manipulate Jimmy and extract a confession. However, I believe that Chuck would've done the same if his illness was real to begin with (e.g. cancer).

While Chuck has used his illness as a means to the goal of getting Jimmy to stop practicing law; his illness did not originate as a means to that achieve that goal.

However, if I may rephrase your question:

Has Chuck exacerbated his illness and the amount of attention he requires (groceries, help around the house, ...) in order to hinder Jimmy's day job as a lawyer?

It's possible. But then again, Chuck seems just as needy when he relies on Ernie, when Jimmy is no longer affected by Chuck's neediness.

Jimmy seems to swing by Chuck's before or after work. He also doesn't particularly keep to a 9-to-5 schedule (nor any other lawyer in the show, for that matter), so it seems unlikely that Chuck expected Jimmy to work less hours as a lawyer because he did chores for Chuck.
More likely, Jimmy would simply work at night if he had been busy for Chuck during the day. We see many cases of lawyers (most notably Kim and Jimmy) work long hours because they are dedicated to their jobs.

So I think the following would be an accurate summary:

• Chuck's disease is mental, not physical.
• Chuck honestly believes the disease is real.
• Chuck asks for help because of his limitations due to the disease. Chuck is a generally self-absorbed person, and does not acknowledge that he is asking too much of Jimmy/Ernie. Whether he knows that he's asking too much seems unclear at the moment, but I don't think he does, based on how he treats Ernie. He has no reason to spite Ernie, and he seems honest (though arrogant) in the help he requires from Ernie.
• Chuck manipulates Jimmy, because he secretly hates that Jimmy is a lawyer. He uses anything at his disposal. That includes exacerbating the effect his disease has on him; because Jimmy cares about Chuck.
• Jimmy wants to help Chuck regardless of whether the disease is real or not. Jimmy helps (and even forgives) Chuck because of brotherly love.

In the episode RICO (S01E08), Jimmy informs his brother that he passed the bar while we can see his brother not ill.

Chuck is the picture of health, sitting in his corner office amidst various forms of electricity. He's even using a Dictaphone to compose a letter. Jimmy timidly interrupts and reveals that he passed the New Mexico Bar Exam ( . . . ). He asks if he can come work at HHM once he is sworn in. Chuck tells him that he has to confer with the other partners, but signals optimism: "How can they say no?". Later that day, Jimmy celebrates with his fellow mailroom employees and Kim. Howard Hamlin stops by the party and -- after the others have left -- informs Jimmy that HHM will not be hiring him.

So Chuck developed his illness while Jimmy was already a lawyer.

In the episode Chicanery (S03E05), it is revealed that Chuck's condition is a mental illness he started to develop after his divorce.

Also, in Chuck's page, you can read that

Jimmy suggests that Chuck developed his condition in response to his divorce from his wife.