Tom's external conflict is his attempt to retrieve the paper that flies out of his window. He has spent all of his free time working on this research in order to get a promotion at his job. In doing so, Tom has neglected his wife, putting his work above their relationship and marriage. Tom climbs out onto the ledge and almost falls eleven stories trying to get the paper back. It is at this point that he realizes he has spent too much of his time trying to get ahead instead of enjoying life with his wife and accomplishing something of importance in his life. This is his internal conflict. When Tom does get his paper and reaches the window of his apartment, the windowm slams shut, and he must overcome this new obstacle.
To me, the external conflict is between Tom and the building. It is between Tom and death. He is out there on the ledge, fighting against death.
This causes an internal conflict. It causes him to start thinking about what is really important in his life. He comes to question whether he is spending too much time and emotional energy on his work. He has to decide whether his work is more important than his personal life.
I think the new obstacle you are talking about is when the paper flies out the window. Now he has to do it all over again.
Tom's external conflict is with the building. He must pit his strength against a massive, man-made structure by balancing himself on the ledge, eleven stories above street-level. Carefully, he must make his way along this ledge while he presses his body tightly to the building for support.
Then, he must carefully make his way around the corner of the building and bend his body to retrieve the important paper that lies between his feet. During this time, Tom can see the Loew's theater sign, miles of traffic signals, countless neon signs, and numerous black dots of people below him.
After he retrieves the paper, he has to decide whether he will make his way back and how he will manage to do so. The external struggle with the building has caused an internal conflict between himself and his fears. Should he stop moving back towards his apartment, he will very likely stumble and fall to his death: considering that his strength is fast failing, there is no way he can hold on indefinitely. However, if he decides to make the arduous journey back to his apartment, his remaining strength will be taxed to the limit.
In the end, Tom resolves his inner conflict "out of utter necessity." He forces himself to ignore his terror and to move slowly back along the ledge towards his apartment window. Eventually, he does reach the window, but he loses his balance. In trying to regain his equilibrium, he grabs the edging of the window, but the "direct downward pull of his sagging body" causes the window to slam shut.
This event causes a new obstacle in Tom's journey. Now, he has to get the window open before he can get into his apartment. However, he knows that he is at a disadvantage here; based on the construction of the window, there's no way he can get enough of a grip on it to open it. He wrestles with the idea of waiting until his wife comes home. However, he soon remembers that it will be fully four hours until he sees her.
Next, he tries dropping coins and lighting up papers to draw someone's attention. However, no one notices him at all. Finally, knowing that "he could not kneel... hesitating indefinitely till he lost all courage to act," he decides that he will use his free arm to break through the window glass. Yelling his wife's name as a war-cry, he rears his hand back and manages to break through the glass. Within minutes, he is inside the apartment. Once inside, he gets out his topcoat and hat and leaves for the theater; the fact that the yellow paper flies out again when he closes the door is immaterial to the wiser Tom.