Grief, be it the loss of a friend, family member, OR pet, is difficult. Don't avoid those feelings, embrace & accept them.
The pain can seem unbearable, but it is not. Many times we avoid the emotions associated with loss and tell ourselves "I'm strong", "I can take it", or "I'll deal with this later". Not a good idea. Although difficult and painful, if you do not let yourself experience the emotions (anger, depression, guilt, etc.) now, they will catch up with you later, when you least expect it. That is called avoidance. I am not saying that you should wallow in your grief or pity, and there definitely are limits on how long you should grieve, but experience the emotions naturally in order to heal.
The opposite of avoiding grief is lingering in it. You should experience the emotions as long as they last. Do not avoid them, but do not hold on to them any longer than necessary. You will never totally get over the loss of someone you love, and you should not, but the pain will ease with time IF you allow yourself to experience the pain naturally and in the present.