Wow, well you're doing what they told you to do.
I'm a bit sceptical about not taking it with milk though. Is it possible to phone your doctor's office and ask them specifically about that? It would be so much better for your health if you could stop feeling so ill so that you can continue to take this medication.
Of course, Ellie, this all might be just tipping you over the edge with the nausea. I'm not familiar with Lyme I'm sorry to say (apart from general knowledge from people who've had it) but would wonder if you would be feeling like that even if you were not on the Doxycycline? Is Doxycycline the treatment for Lyme these days??? I wasn't even aware of that.
You can't afford to get weaker and weaker. You've had such a tough year. It all sounds extremely worrying for you.