I'm sorry this is painful for you. I empathize with how you're feeling, I know I'd feel the same way. It's okay to miss him and want to connect. In my case, my T encourages me to email anytime, whatever I want, so I personally would email him in that situation and if your T is welcoming to emails too I would if it would make you feel better. I don't really see emails as bothering unless someone sends like 20 a day or something, because Ts can check them at their own convenience.

Just consider that he might really be very sick--not to say that to scare you, just that he might not even be up to responding at all and is needing to rest which is why he hasn't gotten back to you yet. But he's not going to forget about you. I hope he gets to feeling better soon and you'll hear from him.