Property Tax Hearing Advice

Hello, I have some concerns with the property appraised value for 2022.

So, here is some backstory, we purchased our first home in 2021 in Houston, Texas and we were house hunting while living in the East Coast. Every offer we made failed but, finally another house that we wanted was on the market for $295k and in order to beat the competition, we had to offer $12k more from out of pocket. So, we were able to buy our very first house with $307k, but that was after May 15th last year so we were not able to protest for property taxes and couldn't get the homestead exemption of $25K, so we paid the full property taxes which was based on $259,506 value which was 10% more from 2020. Okay, fine, we dealt with it.

But, 2022, our property appraised value and market value was increased to $361,146, which is a 39.2% increase from 2021. We hadn't done any improvements on our house yet (this house was built in 2001). So we didn't understand where this price was coming from. And We didn't even try to get the appraisal value, but I guess they do it yearly unlike the East Coast. So we were caught off guard.

Instead of using a property tax service for protesting property tax, we decided to do it by ourselves and they offered us $307k from $361k which is pretty good but still 18% higher from 2021.

So, the real question is that, we are not sure whether we should remain satisfied with this number or wait for our hearing in person. The email said "This offer is valid up until the day prior to your scheduled formal hearing date." Which made us assume we would lose the change altogether to keep the $307K if we try to fight and lower it even more.

Should we wait for the hearing to protest to lower it even more ? or should we just sign for the $307k?

I don't know how our house which is smallest of our neighborhood and one of the oldest deserved to pay more in property tax by that much. We have summited many pictures and documents to support our arguments for the ifile related to the problems of our house. and we probably have nothing more to bring with us besides our voices talking to them in person.

We are just looking for any advice and thank you for your time.