Hi, Why would you want to use another agent to make a new higher offer???
It seems that your first offer was not the only one and then they went through inspection or the buyers backed out for other reasons, who knows....

But I do not see any reason for you to use another agent (this was your buyers agent, I am assuming...
an agent who is working for YOU who presented your first offer, that was rejected by the Seller throught the sellers' Realtor (the listing agent of the property), correct...

You can just contact YOUR agent and ask to present a new offer.... if now the Seller does not have another offer at hand, and the offer they accepted (may be for other reasons than the price, could have been other terms, a higher down payment, faster closing whatever!) fell through, they may just consider your original price you offered or at least negotiate it up with you and then you still have time to have an inspection done etc. etc.

In your situation I would sit down with your Agent (did you sign a buyer representation contract with your original agent?) discuss the situation and see what your agent knows, and then proceed with an offer!

Good Luck to you!

Edith Karoline - YourRealtor4Life!
Working always in the very BEST interest of her clients ...
EdithSellsHomes@gmail.com

By the way if you know of anyone thinking of buying / selling Property in the city of Chicago or any of the Northern/Northwestern suburbs or anywhere on the Northshore, refer them to me and I promise them first class real estate services... THKS!