Can i ask for help from a college prof? A few weeks ago I told my college professor that im depressed. She said I can go to her at anytime if i need help. 

Then my psychologist kicked me out, because I didnt want to tell her the details of sexual abuse.

Can I ask my prof to help me find a therapist? Or it would be awkward/it would be a burden for her? 
I really like her, it felt really good, when she offered her help. I just dont know if she truly meant that i can ask her for help, or just said it...
As long as you recognize that the prof isn't a mental health professional and don't expect her to go beyond her expertise, it would be fine to ask her for help. Especially if what you want is help in finding a proper therapist. 

Professors (many, at least) try to be helpful and supportive in such situations, even though solutions are beyond them. 

But it is probably a mistake to overload your relationship with her with personal issues. Separating the personal from the professional is normally the right course. 

However, your university may also have an office that provides personal support and might also be helpful in finding a compatible advisor. 

Finally, if sexual abuse is an issue, then you should think about other avenues so that it stops. Again, the university may be able to help if it is related to actions taken there.