It is likely that your 10-month-old daughter has secretions draining into her eyes. A recommended solution for this is to use a nasal hygiene technique with a saline solution for babies. This technique can be done up to 5 times a day. It is important to be gentle when using the solution, and using a slightly warm saline solution may make it more comfortable for your child. Over time, they will become more accustomed to this technique, which is effective in preventing complications. If you have any further questions, feel free to ask.