My son had trouble latching on and on day three, his pediatrician said I should give up and start feeding formula. I called the hospital's lactation consultant in tears and she saved my sanity. She gave me a nipple shield. This is a miracle device! Not only does it help the baby develop proper latch-on, it also trains your nipples to be the correct shape for baby to latch-on to. Medela also makes this nipple guards that you wear under your bra. It's got a little hole for your nipple to go through and a plastic dome that protects your clothes. For most of our lives, we are taught to wear things that prevent our nipples from standing out and when we try to breastfeed, that kind of comes back to bite us. I also would pump from one side while I nursed on the other. This was to build up my supply in those early months when it matters so much. For the first two and a half months, my son would only breastfeed with the nipple shield. I bought about four more and resolved myself to that being the way we'd have to do it. Then one day, he knocked the sheild off and never needed it again. He is now almost 15 months with a mouth full of teeth and still breastfeeds frequently. (No issues with the teeth & biting either, so maybe the nipple sheild helped there too.)
At 10 weeks, a baby's stomach is still very small. There's also a point where a baby's suckling is for comfort rather than milk, and then the baby's asleep. It is very common. Don't worry that he's wasting milk. If he were still hungry, he'd stay awake and eat. It looks like he's wasting more than he is. This is especially apparent if you're suffering from mastisis and he's still gaining weight. I know its not fun, but you may want to pump more. My routine was, I would pump from the left while my son fed from the right. When he was done (asleep) I would pump what remained in the right. Next feeding, I'd alternate breasts. I threw the extra milk in the deep freezer and held on to it until my worries about my supply were gone. Also, when you are in the shower, lean forward and massage your breast one at a time. Some milk will probably come out, but it's OK.
This won't last forever. I promise you. Just keep telling yourself it will be OK, and don't ever be slow to ask for help. THis whole thing is not as instinctive and natural as many would want you to believe, but it's totally worth it. :-)