I haven't found any hard scientific research that either proves or disproves the theory that it is best to not drink either 30 mins before or 30 mins after a meal. There is variance among doctors from those that don't really think it is that important, to those who say you can drink right up to the meal, but you should way 30-60 mins after, etc. I've also read differing reasons why it is often suggested. One of the more common reasons I've read what that drinking with a meal tends to wash food out of the stomach and into the intestines more quickly and you won't get the "full" feeling, which may lead to over-eating. Generally, it is usually better for satiation, for most people, to have the food progress through the stomach and digestive tract as slowly as possible. This maximizes signals to your brain that you've gotten enough to eat. There are hormones triggered in the stomach and through the intestines that send these signals. One theory is that drinking with a meal rushes this process.
My personal experience has been that I "feel" like I'm not quite as satisfied after a meal if I've been drinking throughout it. I've never noticed any uncomfortable feelings either drinking up to the moment before I ate, or if I had some drinks while I ate, or right after. I know that some people feel uncomfortable if they drink and eat. So far, I have not had that problem.
If I were in your shoes, I'd probably eat a bit, drink enough to swallow my pills, and then eat the rest of the meal without drinking until 30 or so minutes afterward. I think there is a benefit to limiting liquid intake during a meal and afterward to let as much of the digestive process happen in your stomach and then slowly through the intestine as possible. Again, however, I haven't seen any strong research that really backs this up. So take it with a grain of salt.