Is My 1732 Pillar Dollar Real?

It's fake. That coin is highly counterfeited.

The "coin" is more of a replica than a counterfeit. The design is completely incorrect and was not made well enough to fool collectors who are aware of what genuine coins should look like.

Among other things the edge is reeded. That action - reeding the edge - was a way of evading the law during the 1950s when these types first started appearing for sale.

Reeding is a relatively modern way of edging a coin and requires a closed collar coining press. The US only converted to that type of press in 1836 for larger coins.

I hope the coin came to you at a very low cost - it is a $1 type thing.