I can see it from your GPs point of view - but this advice is out of date and is not best practice. The NICE guidelines say that mums who are breastfeeding children with allergies should be given information about exclusion diets. Breastfeeding is best for allergic babies, even though the formula companies are the ones providing most information to GPs about allergies at the moment.
The most common allergens are the ones listed by packedlunch above, with dairy and eggs being by far the most common in babies. You will struggle to eliminate all of these at once so might be best to start with dairy and eggs. Like packedlunch, I followed an extreme exclusion diet for a long time, and it worked for us - but it turned out that my baby was also reacting to other things (bananas, onions, lentils, tomatoes, apricots, all sorts of seemingly random foods!)
Keep a food diary, with details of absolutely everything you eat, including what flavour jam you are using on your toast etc. This will help you to trace any patterns of symptoms back to their source weeks later. Try not to eat the same things every day - for example, if you are suspicious of wheat, live on rice instead for a bit and then consult your diary to see if there has been any improvement.
Overactive letdown / too much foremilk might account for green poos to some extent, but does not explain the blood in stools, so you and your doctor are right to be concerned.
I would see a different GP if possible, and ask for a referral to a paediatrician with some specialism in allergies and intolerances.