I do not know exactly what the public's role is in congressional decision-making in the modern House of Representatives. Does the public's role means the role of interest groups or the role of private citizens?

The role of the public in decision-making in the House of Representatives is generally meant to mean individuals, but certainly people in special interest groups are members of the public, too, so it would be accurate to say they are part of the "public." 
Individuals are at least superficially encouraged to get in touch with their representatives, all of whom must maintain a local presence in their respective districts with staff to respond to their constituents.  Often in high school civics classes, students will be assigned to find out who their representatives are and to write letters about a problem of general concern in their district. It is the wise representative who writes back! When there are campaigns on various issues, the campaigners will almost always advise people to write to their senators and representatives to express their opinions on the matter, for matters such as environmental concerns or funding Planned Parenthood.  Most representatives get in touch with their constituents routinely, with mailings or emails to inform them of their latest efforts, and to encourage a dialogue.  And representatives do pay attention to what their constituents think, even though they don't always vote the way some want them to.  They also take polls on various issues and sometimes will vote on a bill in accordance with what the majority of their districts wants.  I don't think anyone should ever hesitate to get in touch with his or her representative on any matter that representative is going to be voting on.  It is part of their job description to listen to their public.  
Special interest groups are usually represented to interact with Congress by one person or a few people, whom we call lobbyists.  Nevertheless, they comprise individual members of the public.  These members of the public have banded together for some common cause, and the fact that they have banded together should by no means take away their right to try to influence what their representatives will do. People are troubled by lobbying, particularly when it is very wealthy interest groups who are trying to exert influence, but I don't think you can have a democracy in which some members of the public can try to exert influence while others cannot because they have more money and have joined together.  It is not reasonable for us to be able to pick and choose this way. 
So, individual members of the public can and do affect the decision-making in the House of Representatives.  But special interest groups do, too, and they are part of the public. 
https://www.thoughtco.com/house-of-representatives-3322270