I can totally relate to almost everything you wrote. I feel embarrassed and ashamed about loving my T. I understand loving family, friends, and pets, but loving my T who is my age just feels odd. My family rarely said "love", and now the word is passed around all the time without a deeper meaning. So to actually express a true feeling of love is difficult.
I talked to my T awhile back about love. I asked her to define love, if she loved me, if I loved her. She told me that most languages over simplify the meaning of love. She also said that each person has their own definition of love. So she told me that I needed to define it for myself. She didn't tell me if she loved me, but it's okay if I perceive her to. She told me to reflect more on my definition of love and bring it up in the future.
My T has said to me that she wants me to feel safe and loved when I'm with her, and she has said that her concern comes from a place of love. I asked her to confirm if that's what I heard and she said she did say those things. But she also said she would leave it up to me to interrupt it.
I do not find your relationship with your T to be weird or abnormal. Love is an important part of life, so why not discuss it in therapy? And I am one that believes that touch can be very therapeutic.
I have never directly said or written "I love you" to my T. I'm not ready yet and am still trying to define what love means to me. But I do think it can and should be discussed in therapy.
And you're not alone about feeling fear and shame about it