No, it is not normal to feel this empty. No. You shouldn’t live with it. I’m very, very glad you wrote to us.
I can’t give you a diagnosis on the basis of a letter but I can tell you that what you report is consistent with a diagnosis of depression. It makes sense to me that you feel better when you push yourself physically or take ice baths. Both produce endorphins, a natural “anti-depressant” of sorts. The dogs give you unconditional love and don’t expect anything of you other than your affection. It makes sense to me that being with them also makes you feel better.
All that being said, as you are finding out, it is not enough. What you need now is a professional evaluation by a mental health provider. That person can help you decide if medication might be helpful. You are not obligated to follow the recommendations. However, the conversation will help you understand what is going on and will offer you alternatives to help you feel better.
Usually the treatment of choice for someone who feels as you do is a combination of medication for a while and talk therapy. The medication may give you some relief once it reaches a therapeutic level, but you also need to learn other ways to feel good about yourself and just to feel good besides pushing your body to physical extremes.
Please follow up and get yourself an evaluation. Learning how to take better care of yourself emotionally as well as physically will set you on a path for a much happier and healthier future.
I wish you well.