I like heels and wear 2" to 3" (5 to 7.5 cm) heels to work nearly every day. I do not, however, wear platforms.
It takes practice and is a different "walk" than walking in athletic shoes, work boots or flats.
Try a a lower heel (1.5" to 2") first, instead of something high. Stand up; when you feel comfortable standing, walk "heel, toe; heel, toe" and take a few steps. Walk around in them in your house until you no longer feel like a dork. If you try 2 or 3 times and never get comfortable standing or walking in them, return them and try another pair. (By practicing in your house and not wearing them outside, the soles won't be scuffed & the shoes should still be eligible for return.)
If you try to walk the same in them as with sneakers, you'll clomp like the aforementioned drunken gorilla (good visual; a nice change from my usual "spastic cat" image).
It's easier to walk in high heeled shoes that are not also platform shoes; many pumps and wedges currently "on trend" have at least a 1" platform. The platform distorts your sense of where the ground is.
Look at the sole; if it's a smooth sole, the shoe will be "slick" which is good for dancing but not so much for walking.
Cheap shoes in general, specifically cheap high heels, *will* make your feet hurt. No matter what the shoe cost, if it doesn't feel good in the store, it won't feel better at home.
I prefer a brand called Aerosoles; they can be found new for much less than their retail asking price on ebay and amazon.