TBH what you're feeling is actually very normal, and it's something a lot of us experience: as we start to visibly transition, our dysphoria over our mismatching body parts can actually increase, as can our impatience to have everything match correctly. I'm sorry this is happening to you because it's horrible when you're going through it, but it can improve with time (for me, it took about a year for this stage to ease off). But at this stage, it's all about finding the right coping mechanisms to help you through it.
I don't know whether this will help you, but one of the things I used to do to help with my bathroom dysphoria was to lay facecloths over the bits I didn't want to see when I was in the bath. Then I'd just give it a quick wipe with that facecloth immediately before getting out of the bath, so that I didn't have to spend too much time paying attention to it.
You could also wear underwear or even a pretty pair of loose shorts in the bath so that it's less obvious. Also, bathing at night with the main light out but with a couple of candles (and perhaps a glass of wine) to give you a nice atmosphere in the bathroom can be very helpful. I also removed all mirrors from my bathroom so I wouldn't catch any unwanted reflections. In short: I tried to get rid of accidental exposure to the things I didn't want to see, and I tried to make these occasions more of a treat so it would be more difficult for me to get upset.
As for your other problem: I recommend going back to your doctor and telling them that it's not possible for you to drain it yourself and you'll need an alternative method of doing it. I presume you've been given antibiotics etc. to treat the infection, so if it needs to be drained and you can't do it yourself, you might have to ask for it to be done in hospital. Surely there's another way they can do this...