Since you are at the last minute here and are dealing with an issue of the morning.... There is not a lot of options for you. My short term advice is totally different than if it were long term. For tomorrow.... Can you pump a bottle late tonight? It may mean getting up in the middle of the night but if you are really worried, then you will just have to get up & pump a bottle. This evening will not work because due to prolactin hormones being lower in the evening; you will not get enough milk. I do not suggest you introducing whole milk at 10 minths. Babies some time between 10 1/2 & 11 1/2 months is when they can start processing the cow's milk protien. When does it happen, we can not give you an exact date; so therefore we have come to the 1 year rule because we know it has happen by then for all all typical babies. So you may hear people say my baby tolerated whole milk fine at 10 1/2 months, well guess what, they just by luck ended up with the baby who processed the ability earlier than many. So I would not suggest that. If you had milk stored, I would suggest you mix the breast milk with formula, but since you have depleated your stored supply and only have hours to come to a solution, I would just suggest a pumped bottle for the bed time bottle. During the day, she can try the formula and the bedtime bottle can be the "ole faithful". I would also suggest having her offer the formula in a cup. Sometimes this experience works for babies. Now note, some babies do better with the sippy cups that pour and not suck. Have you tried Good Start formula. The milk is thinner like breast milk and many breastfed babies do a better transition with it.
Now koodos to you for providing your baby the most wonderful gift a mom can give other than life for all of these months. You have done an award winning act.... Good for you A.! Do not stress over it htough. Babies will not starve and will not over eat as long as it is provided. So relax, take a breath and know that he is thriving and just having an opinion at an early age... (((HUGS)))!