You do not qualify for a work permit based on having a Canadian boyfriend and not even if you were common law or married. After you qualify as common law and he applies to sponsor you, if he applies inland (you staying in Canada) and he applies for an open work permit for you at the same time, if all goes well, you could have that work permit in about 6 months.
Currently, you would only qualify for a work permit if an employer applies for a labour market opinion in order to hire you. If you have no special skills, most employers will not bother because in order to get it, they have to prove that they need to hire you and that they can't get any Canadians who are qualified. If you do find an employer who is willing to apply for the LMO and they get it, then you can apply for a work permit based on that and you would only be allowed to work for that employer.
Currently, you would only qualify for a work permit if an employer applies for a labour market opinion in order to hire you. If you have no special skills, most employers will not bother because in order to get it, they have to prove that they need to hire you and that they can't get any Canadians who are qualified. If you do find an employer who is willing to apply for the LMO and they get it, then you can apply for a work permit based on that and you would only be allowed to work for that employer.