It feels to me like the media has taken a medical term that should carry no implicit moral or value judgement, added a load of unhelpful connotations and associated images and ideas, and used it as one of several tools in features and programmes intended to shock and disgust people (and to almost "other" the obese as those awful people over there, not you, you're probably fine, keep watching our content, it's not about you, it's them that's the problem).
I probably look more like the women in the photos that come up on your search, so I know that when serious medical experts are on my TV or radio discussing obesity, it's information that concerns me (and to a greater extent than for those who are only just obese, because where the individual risks of health concerns really ramp up is as you get towards morbidly obese, hence the name). But the twisting and misrepresentation of the meaning of the term means that lots of people who fit in that category are misled into thinking it doesn't apply to them, and they're left in the dark. The extreme negative valence the word has gained means people are horrified, upset and may even deny it if they're informed that they're categorised as obese.
IMO the way the media has used "obese" over the last couple of decades fucks over both people who are only just inside the category, like you, and people who are well inside it, like me.
The numbers say you're in the obese category. Okay, that's a necessary but essentially arbitrary medical category used for population purposes as well as some limited aspects of individual healthcare etc. It's the same as if the numbers said you were hypertensive, or hypothyroid. The line is drawn in whatever place, worked out by researchers and statisticians, and it may be useful information for you and any medical professionals who need to help you. It's no fucker else's concern or business.
If it helps, you could repeat the word "obese" to yourself for a minute, concentrating on the way it sounds, until it starts to feel like the random collection of awkward mouth sounds signifying a once-abstruse Latinate medical term that it really is?
But I agree with above posts saying that the fact you're breastfeeding is relevant — I'm not convinced those lines were drawn with recent pregnancy and lactating breasts in mind.