External hard drive switched its formatting?

First time poster here...please go easy on me if this has been discussed before. I have not been able to find this issue in the forums so I am posting a new thread. Here we go...

Last year I bought a Seagate 1TB external hard drive that promised it will work on both Mac and PC. I had a Macbook Pro at that time for personal use and a Windows PC for work, so I bought something that would serve both. I formatted it as per the instructions and the hard drive worked fine for many months. Fast forward to this year, I got rid of the Macbook Pro and bought a Macbook Air. In between these two Macbooks I used a PC for two months. I connected the hard drive to a PC and it worked fine.

Today I connect the hard drive to my Macbook Air and it says I can only read. I can access all my files, but I cannot write or modify any of them. I checked the formatting of the drive on "info" and it says the drive is formatted to NTFS. How did this happen without my knowledge? Did the hard drive switch its formatting when I was not looking? What I cannot figure out is that I was using this hard drive perfectly fine on Mac and PC for a while....this problem just showed up today.

Please help. How do I change the drive from read only to read and write? There is no "lock" sign under the permissions section. I read up on google and most of the suggestions say that I have to reformat the drive. Is there any other option?

Please and thank you!

Evidently somewhere along the way, Windows decided to re-format the drive to NTFS. It couldn't have happened without your knowledge, however. It just got by you. Anyway, let's solve the problem:

Download and install Paragon NTFS from Paragon software. It's a very reliable driver for OS X that will enable you to read and write to NTFS and is the only driver we recommend. However, it's not free but well worth the $19.95 registration fee.