that sounds like it to me...
FWIW I'll give you ds1's story, the other two have been df from birth on the paed consultant's advice.
He was always a "colicky" baby, I bf him for 10 mo but had tons and tons of cows milk products myself, with no clue about any of this, it wasn't even suspected. Being my first baby, I had no idea that him doing permanently green liquid poo was out of the ordinary and he could projectile poo the length of a room. At night he would only settle laid over someone's arm with their hand in his stomach. his legs were never still and it was obvious that he was permanently in pain. He just screamed all the time. When he was about 10-11mo I stopped bfing him, and his symptoms became worse, eczema all over his body too, but still we had no clue. I could only get him on to the first baby milk, he wouldn't tolerate the 'follow on' milks. Every time we went on holiday we ended up taking him to hospital or calling doctors out because he had what appeared to be food poisoning (which of course is exactly what it was to his system) because we were giving him the baby milk which comes pre-prepared in cartons, and is apparently more concentrated. He used to just hang over the side of the pram, his nose running, with no energy One holiday when he was 18mo was particularly bad, we came home because he was so ill, and my mother said "It's that milk, you know!". So we took him off it. We know someone who keeps goats and she told us to try goat milk as she supplied a local nursing home for their patients who had ulcers and digestive disorders. We tried it. His eczema was gone within three days and he was a different child within a week. He hadn't put any weight on from 10 to 21 months, and it was a long struggle from there to get the weight on him but as his system heals he absorbs better and is a nice weight for his height now (he's 8.6yo)
Blood tests show a high IGE (allergy factor) but strangely it doesn't appear to be to anything specific - obv we know that it is to milk, but the tests don't show it. Even now I'm not convinced that he absorbs all that he should from his food and he is often shown as anaemic in blood tests - and I am assured by dieticians that he has a fantastic diet so this isn't the cause.
The blood tests aren't nice for a little child, but they do put the 'magic' cream (local anaesthetic cream) on their skin to stop it from hurting them. If you are sure that this will get you an answer, then go for it - but if it's doubtful then look into other options.