I'm a Board Certified Lactation Consultant and I've seen of lot of cases of thrush and even had it myself. However, it is tricky to diagnose. Most MDs have been trained on formula fed babies and are used to much more severe thrush symptoms, such as the "cottage cheese" stuff coming out of the mouth and onto the cheeks. Breast fed babies have much milder symptoms and IMO, seeing a Private Practice Lactation Consultant ASAP is your best bet.
There are a lot of treatments for thrush and I've tried them all. IMO, Diflucan for both mom and baby for 7-10 days will clear up the thrush the best. In most of the USA, most yeast strains are resistant to Nystatin (but MDs continue to prescribe it because that's what they were taught to do in Med School) but with the help of a good IBCLC you can get proper treatment IF it is thrush.
One of the things about thrush: If baby has it, Mama has it, if Mama has it, Baby has it. Either way, you both need to be treated, and I prefer systemic treatment (with something like Diflucan) to topical treatment (with something like Nystatin) Old remedies like yogurt, vinegar water, Tea Tree Oil etc do not usually get all the yeast and can leave you and baby in pain for months. (Plus, I wouldn't put Tea Tree Oil on a sore nipple or into a baby's mouth. I have been in practice for over 20 years and have just seen these old remedies fail again and again and too many Mamas give up breastfeeding, as they were simply using the wrong remedy or trying draconian diets along with them that are very stressful and difficult to stay on, especially when you are already stressed and in pain. Thrush can be painful and persistent so I always have my clients go with the Gold Standard from the start. (Diflucan) Sadly, you need prescriptions for this medication.
I use an alternative with my clients whose doctors won't treat properly for thrush and the few left who don't believe Mom can get it from baby: There is an OTC remedy called Gentian Violet. It is a dye that has anti-infective and anti-fungal properties.Most private pharmacies and some internet places carry it. My method: 0.5% Gentian Violet. If you can only find 1%, dilute the amount you will use for one day's treatment 50/50 with sterile water (you can boil bottled water for 5 minutes and then cool it for this.) Mix up enough Gentian (with H2O if needed) and place a few ml in a small disposable medicine cup. Take a Q Tip and PAINT the entire inside of the Baby's mouth with the Gentian. Get the insides of the little chubby cheeks, the gums, under the tongue, the roof of the mouth, everywhere! Then use a clean Q Tip and paint each nipple with the Gentian solution. Do this 2 times a day for NO MORE than 3 days. Wear raggy clothes and disposable breast pads when you do this. If you can get raggy old T Shirts for the baby to wear all the better. This stuff stains like nothing else. Everything you wear will be Tie Dyed Gentian Violet.
You can also use some 1% hydrocortisone ointment AFTER the Gentian treatment 3 days is over, if you are still sore. OTC yeast infection cream or ointment can also be used, I usually use Clotrimizole for vaginal yeast infections. It tastes terrible, but you only use a paper thin layer. Buy the "Three Day Treatment." as this has the right concentration of Clotrimizole that is not too strong yet not so weak that it won't work.
Diagnosing over the internet is tricky and could easily miss things, so I'd see a Lactation Consultant for verification and treatment options. She can also check the latch and the baby's oral structure to make sure nothing here is contributing to the problem.
These suggestions are based on peer reviewed methods and the experience of thousands of breastfeeding mothers and the lactation consultants and LLL leader who have helped them. It is not meant to take the place of getting proper professional guidance. As with all things, common sense is to be used.