Here is a description of depression. Read it and see if you think this applies to you. It's not normal to be completely without emotion. Your emotions are there - you've just buried them deep within you. And yes, it could have started when you lost your dog. For most people, their pets are their children - their heart and soul - and when you lose one, it just rips your heart out. Sometimes it hurts so much, that it becomes easier to block out the feelings, rather than deal with them.
Depression is a state of low mood and aversion to activity that can affect a person's thoughts, behavior, feelings and sense of well-being. People with depressed mood can feel sad, anxious, empty, hopeless, helpless, worthless, guilty, irritable, ashamed or restless. They may lose interest in activities that were once pleasurable, experience loss of appetite or overeating, have problems concentrating, remembering details or making decisions, and may contemplate, attempt or commit suicide. Insomnia, excessive sleeping, fatigue, aches, pains, digestive problems or reduced energy may also be present.
Depressed mood is a feature of some psychiatric syndromes such as major depressive disorder, but it may also be a normal reaction to life events such as grief, a symptom of some bodily ailments or a side effect of some drugs and medical treatments.
If I were you, I would start a journal and just write down what happened today, what encounters you had with people, how that made you feel, etc. It might be that when you start writing down how you feel, you will feel safer revealing it on paper.
Bottling up your emotions can only lead to problems later on. See if you can try and get a handle on this before it gets worse for you. Good luck.