Sounds like you have a separated cartridge casing. You do not need more ammo. If you shot a .308 in the rifle, you need to get it to a gunsmith. Besides the bit of ruptured casing that looks to still be in the chamber, you MAY have done damage to the bolt/ locking lugs. Headspace will be totally wrong on a .308.
IF the rest of the gun is OK, a ruptured shell extractor will usually pull the casing. Any decent sized local gun shop should have the right ammo, and it is easy enuff to order on line- My UPS guy is still not speaking to me after the last order.
What we have here is... failure- to communicate.