Despite my convincing my dog that I am the alpha dog at which point he will cower, he will bare his teeth and bite me when I am trying to give him meds or trying to clean him after a recent bout of bowel problems, I try to hide the meds in food and he spits them out.
As I read your post, I got an impression that your dog does not see you as a trustful and respected leader. I am not convinced with the idea of the owner being the "Alpha dog" and unfortunately your dog's cowering doesn't reflect a good relationship between you and your dog either. If your dog really trusts you, he would let you do whatever you do. Can you clip his nails, brush his teeth, or treat his wound without any fusses? Can you take a toy away from him? Does he respond to your "Leave it" or "Drop it" commands? It is very important that he obeys to those commands. Just imagine you drop your pill on the floor accidently and he is right there. One of the most common reasons for emergency cases is eating people's medicines.
Solving the problem of giving him med is much easier than improving the overall relationship with your dog.
It depending on the size of the med but if it is small enough to swallow, I will wrap it either a small slice of ham or cheese and give it to him by offering another small slice of ham/cheese (this is important!) so that he will hurry up and swallow the wrapped med in order to get another slice
Coincidently I had to give a 10ml of liquid med to each of my dogs last night since one of them had whipworm (Ugh!). If it was a smaller amount I would just squirt it into the mouth when open it with my other hand but 10ml was a bit too much. I ended up mixing it with cottage cheese and each of my dog just ate it all up. I outwitted them!
I wonder if your dog is scared? If his response to your being dominant is to cower, it sounds likely to me that hes a bit threatened/intimidated by the medication administration.
When you say you have to clean him up after a bowel problem, I'm assuming you mean either a bath or a towelling off? I know a few dogs and animals with a similar problem, and they react badly because they are feeling bad - either because of their medical problem, pain, or feeling back for having an accident and getting themselves dirty.
Overall, try and re-think your approach to your dog. Use soothing, calm tones and dont move suddenly. Be patient, and try to let your dog come to you. When youre cleaning him up, be gentle and say lots of "good boys" when he handles it well. You want him to know he's not in trouble, or being punished. Try giving treats through the whole thing, and lots of breaks for pats.
The medication you give him, is it a pill, or a paste, or a shot? I might be able to help with more ideas if I know what exactly you're doing to medicate him.
In every day tasks, try to encourage confidence and trust with your dog, by giving him lots of scratches, etc. Work on training, even if its just fun stuff. If he starts cowering, take a step back, call him to you, and say "good boy" when he comes. If his reactions to medications are partly based out of fear or getting frightened because of pain or anything, you want him to look to you as a source of comfort, so try to include little moments like this every day to get his confidence up