I Was just let go from my job that i just started the frist of the year. I was told that they couldn't hold my job because I would be out sick for three weeks. I'm in care of a Dr. and did give them a note. I just want to know if this is right? and can I be let go for this?

Since you have been working for them less than three months, there is no protected medical leave available to you so yes, they can terminate you if you are unable to be at work for three weeks, even if it is for a medical reason. Barring FMLA, which does not apply here because you have worked for them for such a short time, a doctor's note has no force in law.