I recently had a massive panic about IBC for two months (I am ok!). I totally feel for you, I know how horrendous my experience was...but here are some things I learned that might help:
As the others said, it is very rare.
I saw two surgeons, an OBGYN, two GPs, two radiologists and and ER doc and all said that the discolouration I had (also on the underside, but more on one side than the other) was hormonal and benign and probably triggered by birth/nursing in my case. (also had multiple ultrasounds, biopsies, mammos, you get the picture!).
In addition to discolouration, I had peau d'orange, and swollen nodes in my armpit. Everything on the net said it could only be disastrous but all the above docs were certain it wasn't. (I did have mastitis as well which coincided with my discovery of the discolouration). It took me a long time to accept they were right, only because of my prior googling, so good on you for not going there
IBC progresses quickly so typically the changes wouldn't be subtle and would be worsening quickly.
Skin on breasts is just like skin anywhere else and can be irritated by heat, detergent, sweat, allergies, infection etc - one thing to think about might be how worried you would be if this was on your arm instead. All the things that can irritate skin are far more common and treatable than anything scary.
I spent a lot of time on an IBC forum and learned that the vast majority of posters who came there worried they had IBC in fact did not.
I hope this helps. As I said, I know how scary it is to worry about these things, but I really hope I've helped. Hang in there. Tuesday will come and you'll be able to get a medical review and we're here for you in the meantime.