Does my case have a good chance of being dropped because I was not read my rights? Now I'm aware that it doesn't usually work that way but in my case prior to the arrest I admitted certain things and I've heard that those things would be inadmissable in court because I was not read my rights. So I want to know if that would be a plus for me based on the fact that if they cannot use my statements againest me then it would be hard to prove the case because what they found could have been anyone's in the house.

NO, at the best, very best what you said may get thrown out and not used against you, the issue, if you give them statements freely before you were a suspect, they are not required to read rights either. You are just watching too much CSI

Being read one's rights is one of the most misunderstood pieces of American law. A law enforcement officer is required to read you your rights at the time of an arrest only. And the only consequence of not being read your rights is that anything you say or the use of anything you say cannot be used in court.

Anything you said prior to your arrest could be used. And anything independently garnered could also be used.