We relocated and purchased our home about a year and 7 months ago in an area that was more expensive than we were coming from. The purchase price was $239,000, we put down $14,000, and took a home equity loan of $34,000 to finance the rest of the purchase price and to avoid PMI. I recently submitted a question about whether or not to start paying down the first mortgage or the home equity loan, and got great advice, but I am wondering now that my tax value of my home has increased in January from $200,000 to $279,000 due to reassessment, (I know it wouldn’t sell for that now because we recently had comparables done in January), would I save money by refinancing my first mortgage and adding in the home equity loan so the total amount has a lower interest rate? My husband thinks we have to wait 2 years before we can refinance, and I’m not sure about that, but that would be this July. My goal is to pay off our house as soon as possible.

Depeding on the terms of your loan, you can actually refinance as soon as 6 months. The best thing to do is to call your mortgage loan holder(s) and just ask!
There should be no problem with refinancing right now.
Nope no problem at all.