HardDrive Suddenly Not Working

I have a 500 GB Fantom Drives external HD. It has been working fine until the other day i tried to use it and my computer does not recognize the HD. I connected it to my computer (USB) turned it on, computer makes the ding noise that means there is something connected, so that's not the problem. The device is turned on and i get the blue light on the HD. I look for it and instead of the drive name i have given it, it only says "Local Drive: G". I attempt to open it and it wont open and it sometimes freezes up my computer. It doesn't give me any information on the drive as if it were empty and unreadable. The only thing that my computer has done is ask me if i would like to format my HD. I said no, properly removed it from my computer and turned it off. This problem started suddenly and the last time i used my hard drive, the night before this issue appeared. I had properly disconnected it from my computer turned it off and hadn't touched it until the morning. The data is VERY valuable to me but if there is anyway i can save 900$ going to a data recovery place that would be amazing, and it would be nice to know if my data is even able to be saved! i don't know a ton about computers but i'm willing to do a lot here and know some CS kids who can help me out... though they aren't hardware junkies... if anyone has any advice please let me know. THANK YOU

I've plugged it back in with restarting my computer a bunch of times, properly removing it each time, i have 4 USB ports tried it in all of them. I even let it sit for a day a tried it again. Still nothing, but thanx for the tip. I'm really scared of losing my data and feel like i should almost just stop touching it so not to make it worse