This is the way I did it with my elder one. He too didn't want to walk on his own and he is too heavy for me to carry, I told him that if he do not want to walk on his own or sit in the stroller, we are not going out or we will not bring him out. Slowly he started to walk on his own as he knows that if he doesn't, he don't get to go out.
If this doesn't work, you can consider getting a soft structured carrier or wraps to do back carry. It will be of lesser strain to your shoulders. Do note that your child is 28 months, she may need a toddler carrier instead of a standard/baby one. Toddler carrier have more support compared to standard/baby ones.
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