I gained 7lbs in 2 weeks. My Dr said that it happens when the baby packs on weight. I haven't gained anything else since the 7lbs. I actually lost a lb. I'm 38 weeks and 2 days. Also protein can be caused from losing your mucus plug. Or at least that's what my Dr told me.
Was your blood pressure ok? Swelling and protein in the urine is not good but only a concern if your blood pressure is high too, as it can be a sign of pre-eclampsia. Drink plenty of water to try get the swelling down and keep your feet and legs elevated to hip level when you can, with support such as a pillow under your knees.
Yes, swelling will show as weight gain.
I gained 12 pounds from Wednesday to Monday. It's swelling but I also have gestational hypertension. My Dr is also checking my urine weekly for preeclampsia. I am 35 weeks now and as long as gestational hypertension don't turn into preeclampsia and my BP meds continue to work I will be induced at 37 weeks.