All of my kids are extremely close in age, and I've definitely been through this quite a few times. Here's one thing I do change, though. When I'm pregnant, and it hurts to pick up my toddlers/kids, I break out the birthing ball. Oh, yes. I can roll it right up to my LO and sit on it, then pick my child up. It keeps the pressure off of my ligaments and pelvis. I will also squat down to my children and hug them instead of picking them up, and much of the time, my kids are happy enough with this and won't ask to be held at that very moment.
The aches and sharp pains will stop soon, for a while, anyway. Then, you can go back to picking up your child like normal. Instead, take it easy as much as possible! Try to pick your child up while sitting, yes. Have your child climb up to you when possible. Your child senses the changes in you. She doesn't understand what's going on and just wants to go to her safe space - which happens to be you.
How wonderful. Now is the perfect time to let your child bond in other ways. If you give your child the amount of attention she needs, the less she will have to go to you to be held. When I'm pregnant and my kids start to get clingier, we spend more time snuggling together and reading books, doing puzzles together (does your 14m old have chunky puzzles? They're great!), singing together, dancing together, etc. So many fun ways to fill your daughter's cup.