Pretty normal for them to be very cranky and crying murder. Stay calm and dont panic. Talk to them normally, it might be cold so you can put small towel while changing diaper over their body. Pàcify them while changing diaper like "Ohhh your diaper wet, it needs to be change, sorry, ill make a quick one okay?" Whatever you think like motherly instinct work ❤
Ah thats totally normal you can keep any flash cards (colourful or black and white) on the side or give them a rattle in hand. divert them by making sounds like dog cat bird etc so they will watch for a while till they get bored by then you will be done changing the diaper. You can start giving them teething toys too as they have turned 3 months old already
its normal for a newborn to cry murder when changing diapers. sometimes they just feel unsafe. but if nwborn crying without any sound you should maybe try and check if there's any discomfort. like stomachgas try to massage baby. while changing you can try and move its leg up and down cycling motion slowly. or just turn baby facing down and rub its back.
Mine cries like murder too so I feel you. I try to distract my baby with rattle / plastic sounds. Sometimes it just doesn’t work and he only quiet down when the pampers is on him.