No answers, sorry!
But just to say that this happens to me too, so big sympathy! However little sleep I get, I still find it difficult to drop off.
I know it's easy to say, but the more you worry about it, the worse it gets. I tend to just listen to my iPod now and accept I might be lying there for a while. Remember, even if you're not sleeping you will be resting, and that is also good.
What I would say is that, from reading here, and from my very limited experience, it seems very normal for a 14 week old baby to wake many times in the night because it's hungry.
To give you hope, my DS has always woken up loads, and I've always just fed him (unless it's, like, half and hour after he fell asleep or whatever). To be honest, it felt easier than fighting with him to sleep without feeding. He always dropped straight off afterwards. And I also didn't want to starve him if he WAS hungry. Sometimes he'd have a big feed, sometimes a little one. Sometimes, I felt it was probably just for comfort, but I decided it didn't matter.
I went through some seriously sleep-deprived times, but I couldn't have done it any other way, personally.
Now, at 6 months, DS is beginning to drop night feeds of his own accord. Often, he only wakes once in the night now.
This may not be what you want to hear!! But hang in there, and catch up with sleep where you can during the day.
With hindsight, these things do pass eventually....