LinkedIn seems puzzling. I am a member of a charity (non-profit) and want to start a LinkedIn group on their behalf. I also have a personal LinkedIn account. I don't want to mix the two.
The non-profit assigned me an email address. When I attempt to register with LinkedIn with that address, LinkedIn re-allocate my personal LinkedIn account to the password I give for that new address - i.e., refuses to accept that I can both have a personal account and a nonprofit account.
Are you using the same email account for both your personal and the charity account? If yes, then change one of them. If you are entering two separate contact details the system has no way to know it's the same person unless you re-use something for both that it deems it as being the same account.