I was told that i could claim my cousin since she lived with me for all of 2020 and I supported her and she is under 18. Is this true

Yes and no.

There are two types of dependents, "Qualifying Children"(QC) and standard ("Qualifying Relative" in IRS parlance even though they don't have to actually be related). There is no income limit for a QC but there is an age limit and student status test, a relationship test and a residence test. Only a QC qualifies a taxpayer for the Earned Income Credit and the Child Tax Credit.

 

A cousin is not considered closely related, so she cannot be a QC.  A person can still be a Qualifying relative dependent, if not a Qualifying Child, if he meets the 6 tests for claiming a dependent:

1. Closely Related OR live with the taxpayer ALL year
2. His/her gross taxable income for the year must be less than $4300 (2020).
3. The taxpayer must have provided more than 1/2 his support

In either case:

4. He must be a US citizen or resident of the US, Canada or Mexico
5. He must not file a joint return with his spouse or be claiming a dependent of his own
6. He must not be the qualifying child of another taxpayer 

, The Other dependent (qualifying relative) credit is worth (up to) $500 per dependent and is non-refundable.  That is, it can only be used to reduce an actual tax liability.