10 weeks is too young to let her cry. Babies nervous systems are still developing for a long time, and it is hard to know what she is physically feeling, but that's all she knows right now, and will know for a while. If you let her cry, you will be missing the reason that she is crying, which could be pain! Yes, babies left to cry will eventually stop, but that is because they are exhausted and defeated, not because the problem is gone. And babies have a need for physical comfort and holding, so that is also a valid need.
If she has a strong need to be held, you may want to try the Native baby carrier. It straps the baby onto you, chest to chest, in a very secure way. Then you have two hands free, you can nurse with it on, and if you lay back, supported, you could even nap with her. It's a complicated set up, but you should be able to leave her on for hours.
For the latching issues, if you can go to a lactation nurse or specialist, I think you will feel better and have some more tools in your toolbox. Internet is great, but talking with someone helpful, knowledgable and compassionate will give you huge relief. She may have thrush, or, another latching issue I just heard of has to do with the thing that attaches our tongue to the base of our mouth. In case she is crying because she is colicky, I heard that the most recent "discoveries" about colic point to a bacteria in the digestive tract, which may be why gripe water helps. I've heard that certain gripe water formulations work better than others, so you may want to research that if you want to try it. Or it may be reflux, in which case there are lots of helpful things, one is not having her lie flat (Native carrier and sleep positioners can help). Also I'm getting the Arm's Reach Cocoon sleeper for my next baby. It moves gently when the baby moves, keeps them at an angle more natural for them, and you can move it around the house easily and have the baby at an angle at which she can see you.
I am of the school of not letting babies cry, and there is lots of evidence to back that this is healthier for the baby, and babies who are not left alone to cry develop into easier, happier, more confident children. You cannot spoil a baby, that is more an issue for older children. It's good that she knows if she cries you will come, even more so than that you know if you yell that someone will come. She can't do ANYTHING for herself. a GREAT, very readable, fascinating book on the physiology of babies and their needs is "Our Babies, Our Selves" which I read while I was nursing. It is a wonderful book.