Haha , Dont worry dude , youre only 2 hours into a 70+hour game , its normal not getting the hang of it , + most people who played it have already played Fallout 3 before so dont worry :) .
Anyway ,
You know if its the main quest by simply understanding the story , you are looking fir the dudes who shot you , anything but that is not main . as for the speech thing , Fallout is all about creating a character that best fits you , and is different from all other characters by all other people , Speech is one of those things , You can concentrate on having a high speech and getting people to help you , OR concentrate more on having a high Guns and do more damage , so its a matter of choice , you imrove your Attributes when you level up , you get points to spend as you want . And the game is abuilt as if you will be perfectly able to finish it with ANY attributes , if you have 0 speech and noone helps you , the quest is just going to take a little longer , but thats okay because you upgraded something other than Speech which will help you in other situations
P.S : If someone on the game asks you a gun related question , your response will be determined by your Guns score not necessarily Speech .
stick with the gun she gave you until you go to the second town (the one with the dinosaur ) where im sure you will find a shop ... even if you dont i stayed with it for a while longer ... And yes you can fix it with some NPCs of you choose a certain dialogue option , or find a weapon similar to it and have a high Repair skill .
Keep in mind that Fallout : NV is AGES above Oblivion , not as in better but it was published many many years after it , so expect a more deep and realistic and complicated experience