Yes, this is me as well. I've been working with my T for 2.5 years and I think about her a lot and am still in 'counting the days between sessions' mode. My thoughts towards T aren't remotely sexual either. The thoughts and feelings about her are like pining for her really, but not in any kind of romantic way. It's more about wanting to be there in the space with her because that feels safe and reassuring and comforting, if that makes sense...? Presumably, ideally i should be able to comfort myself and reassure myself and make myself feel safe on my own, without looking to her/'the space' to do it for me? I'm obviously not there with that stuff yet...
I literally can't wait to go to my session each week, then often get there and clam up so don't get to say what I wanted to say. So, that frustration with myself then maybe makes the intensity of feelings and longing between sessions stronger because it builds from week to week each time I fail to say what I wanted to say and then have to wait another week to try again.
The intensity and pining did actually ease for me for quite a while but is now ramped right up again. I think that's because there's currently some uncertainty about whether we can continue working together, so I think my anxiety around that is manifesting in more thoughts about her and more feelings of desperate clinginess towards her. At the moment, I feel like I am sort of obsessively thinking about her/therapy and that feels unhelpful and unhealthy to me - though, as I said, I think it is being fuelled by high anxiety.
I agree with others that attachment to T is a beneficial, understandable thing and I'm sure thinking about them a lot between sessions is common.
If it feels 'too much' for you though, it may be helpful to bring it up with your T - they are very used to this stuff and a good T won't find it very strange or alarming or respond by firing you.