It's definitely worth trying cutting out suspected foods for a fortnight. If you get withdrawal symptoms (headaches, clumsiness, aches, pains) on days 3 and 4 it's probably food-related. I had to do a dairy-free trial because of bf'ing DS, and discovered I was intolerant to lactose (milk sugars). Changing to lactose-free dairy products boosted my energy levels a lot and improved my IBS considerably.
I've done a couple of gluten-free trials and I have found them both dull and expensive. Things that are normally cheap are really expensive e.g. gluten free oats cost £3.00 for 450g from Tesco. It's worth a try though.
Something else that can cause mood swings, tiredness, sudden irritability is being sensitive to sugar. Your body responds to sugar & white carbs as if they're addictive dcrugs.
There is an eating plan called Radiant Recovery to overcome it. There's a test on the website for how you know if you're sugar sensitive.
I've been doing it about a month after struggling with long-standing irritability, mood swings and exhaustion. I'd tried eliminating dairy, gluten, eggs, nuts, soya, and the GP tested me for iron levels, mal-absorption of nutrients, coeliac disease and thyroid, all of which came back negative apart from the dairy, which helped but didn't solve the problem.
I'm only part-way through the RR plan but it has transformed my energy (and patience) levels by about 500% so far. It has 7 steps, and the first 5 are about adding things to your diet rather than giving things up.