ARE EMAILS BINDING? Newbie here but I haven't seen this discussed

[Michael Payne]

Hello BP family. I could use some insight. I made an offer on a SFR. The agent replied to my offer with a counter by email saying that the owner was elderly and out of town, but when she was back he could have her sign a proper counter offer and send it my way. i accepted the counter and agreed to wait a couple weeks for the seller to get home to receive the signed counter. Two weeks go by and now i'm now being told that there is now a 3rd party in the mix who is offering more money. At this point, my original offer has expired. Should i rewrite it to the email counter price and expect it to be honored? Should i raised my offer because of the 3rd party offer? Has anyone had a similar experience?