Concerned about possible Anemia in baby

I'm concerned my baby may be anemic, 4 of his nails have got a large indent vertically and look like they're starting to go spoon shaped, he also has upped his naps back to 4 a day and yesterday had 5 , he's been extremely irritable but that could be down to teething too, he had blood in his poop on one occasion, we have visited the doctor but the doctor didn't seem to really listen to my concerns and was just smiling at me like he thought I was being over worrying, but I am genuinely concerned , he did mention anemia and the possibility of celiac disease , but then said he can see what I mean but isn't concerned , and wants to see him in 6 weeks , I was hoping for a blood test to fully check he's OK, but he didn't want him to have one , I might be sounding over dramatic but I think there's something wrong, not sure what I'm trying to get out of this but maybe just wondering if anyone else has similar experiences , my partner wants me to ring nhs 111 for second opinion, but I'm contacting the health visitor first to see what they think , thanks for reading