Can my girlfriend kick me out her house after living there for more than 2 years. We also have a child together

Yes, unless you are on the lease/deed.

This is a legal question so has been moved from the Relationships forum.

The answer depends on what you mean by "kick out". If you mean just throwing you and your belongings out of the house with no notice, then no she can't do that. If, however, you mean force you legally to move, then the answer is yes.

After two years you have established residency. Therefore, you have to be treated as any tenant. She needs to give you legal notice to vacate. What legal notice is required depends on where you are (ANY question on law needs to include your general locale as laws vary by area. ) If you refuse, then she goes to court for an eviction order. But she can't just throw you out or lock you out. That would be an illegal eviction and open her up to a lawsuit.

So what is prompting your question?