Yes, It is completely normal! 🙂
You should expect a fair amount of swelling and tightness for the first week or two post op whilst your body is adjusting to the implants.
Everybody is different though. During healing process you may barely swell at all, or you may spend a full week with swollen breasts. I have read so many times about woman using the icing technique to reduce the swelling and i plan to do the same. I bought special ice bags, but i hear even just using ice packs or ice cubes in a sandwich bag covered with a clean tea towel works absolute wonders.
i hope your swelling subsides soon, either way 🙂