Start eating breakfast if you don't already. If you aren't really a breakfast person try out brunch/2 lunches. In high school I didn't really eat breakfast a lot but I would either 1) pack 2 lunches, one to eat at 10am and one to eat at noon or 2) pack food to eat at 10am and eat school lunch at noon. The brunch/first lunch I ate wasn't really all ate at 10am but more of spread out over and hour or two.
I know some runners only drink water, but to add calories start drinking milk and juice. Still drink water but have some non-water beverages with your meals.
Start snacking throughout the day.
Buy some protein powder and try drinking either a regular protein shake (water/milk + powder) or by adding it to smoothies with fruit/greens/etc. Making shakes with milk instead of water will add calories. If you don't like/can't drink milk try milk substitutes (almond, soy, etc.). Drinking your calories can be an effective way to put on weight.
I'm kinda questioning how your coach isn't helping you any with your weight even after you asked him about it as 5' 10" 110 pounds is very much underweight.
I know how tough weight gain can be but it can help your running out a lot. Gaining healthy weight helped me endure (and succeed in) the meat grinder 800 program that was my high school.
Overall, I would suggest talking to a doctor/nutritionist about all of this as they are experts.