Some of these comments are awful.
Yes, breastfeeding can prevent pregnancy, usually by preventing ovulation. The OP believes she has evidence she is ovulating, so presumably was hoping the GP would either say: actually, that evidence doesn't mean you're definitely ovulating, so it would be best to stop breastfeeding, or, actually there are other steps breastfeeding can interfere with like implantation so it would be best to stop breastfeeding, or, hmm, if you're ovulating then it probably isn't the breastfeeding but it might be x y or z so let's do tests for those.
Saying 'it's because you're breastfeeding' but ignoring the fact the OP believes she's ovulating isn't v helpful and just sounds like the GP wasn't listening, nor is the 'African women use it as contraception' line which I agree has some dodgy undertones.
That being said, on my first I tracked my temp which made it look like I was ovulating and I definitely had anovulatory cycles. It's also the case the tests they do are done on certain days which assumes a regular cycle so may not actually be informative. I'm in a somewhat similar position in that I'm still feeding a 22 month old with allergies, but in my case I want to postpone ttc until I wean her which I plan to do at 2 (mostly so I can ttc as I'm late 30s) as I honestly feel like I'm still a bit wiped out from the feeding and my cycles aren't back to normal and I don't want to have to abruptly start weaning.
I'd recommend 'Taking Charge of Your fertility' by Toni weshler, I cant remember if it says much about breastfeeding but it's helpful for all the secondary signs of fertility, eg do you have abundant cervical mucus? My periods have returned, if anything they're more regular than they were before, but I don't have the cervical mucus and I definitely think some months I'm not actually ovulating. I also found it starts with the egg quite useful though a bit intense, and daily yoga.
I think it's easy to underestimate the hormonal effects breastfeeding can have, I don't think it automatically means you need to stop but I wouldn't rule out it having an effect and I'd start looking at ways to ensure you're not deficient in any nutrients, doing some natural things that can help balance your hormones like exercise, yoga. And maybe it's worth having private tests. But as unhelpful as I think the GP is, my personal feeling is a lot of the time there's just a v slight imbalance in hormones that can cause something to go wrong, and breastfeeding may be that little extra pressure on your system throwing it out. It's worth trying other things first, but I wouldn't dismiss the connection out of hand.