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I am sorry to about your new puppy's condition. Yes, deworming him is a good idea as is applying a prescription flea medication (make sure it is safe for puppies that are your puppy's age) as fleas and external parasites are common causes of anemia in puppies. If possible, I also recommend taking him to a veterinarian so his blood can be tested and it can be determined if he needs a blood transfusion. Testing can also be performed to discover the cause of his anemia so that it can be treated.
If his heart rate is high and he is unable to get oxygen to his tissues properly, then he needs a blood transfusion or else he could pass away. Iron injections will take too long to work because this does not actually replace the red blood cells that he has lost it only gives his body iron to make more- that takes time. Iron injections will help him in the longer term but will not work fast enough to save him if he is severely anemic and having a crisis because of it.
Once he is eating well and his red blood cell count is coming, up then you then you can give him an oral supplement (have your vet give you a proper dose based on his current weight as he is a growing puppy and his weight is expected to change) until his red blood cell count has bene normal for several weeks. Also, make sure he is on a dog food that is formulated for growth and complete in nutrition (and continuing with flea prevention) should keep him out of danger in the future.