Correct answers
Lets go with this How was the S3 Prior to Update that you Done was it better was it worse and if you can remember how did it perform out side of the Building you live in) Building's tend to not play nice for some phones and the Samsung's are noted for not having a strong receiver as like in the Motorola's) I'm not knocking them as being totally bad but there Receiver could use a little help..
As for Sim Cards they are very sensitive to 2 things we have in Us: 1. is the Static Electricity 2. Is the Oils that are in our Fingers). We need it to help us Motivate.. but when our fingers come in Contact with the Gold Area of the Sim it can just about Render it useless). It's good thing to remember the Sim Card is the Key to the phone getting the 4G signal and other important stuff with your account & plan..
Since your having the issue with the 4G One thing you could ask for is another Sim Card there electrical and even the brand new ones can go bad i'v had mine installed in my 2 Maxx's for just over a Year & once i Installed them i have yet to Remove them. Knock on wood..
Give what i mention a thought and you might Try a System Cache Clear Followed by a Factory Reset doing one Won't hurt it any more than what it is already doing. Actually it might just help the phone..
Good Luck b33 
Lets go with this How was the S3 Prior to Update that you Done was it better was it worse and if you can remember how did it perform out side of the Building you live in) Building's tend to not play nice for some phones and the Samsung's are noted for not having a strong receiver as like in the Motorola's) I'm not knocking them as being totally bad but there Receiver could use a little help..
As for Sim Cards they are very sensitive to 2 things we have in Us: 1. is the Static Electricity 2. Is the Oils that are in our Fingers). We need it to help us Motivate.. but when our fingers come in Contact with the Gold Area of the Sim it can just about Render it useless). It's good thing to remember the Sim Card is the Key to the phone getting the 4G signal and other important stuff with your account & plan..
Since your having the issue with the 4G One thing you could ask for is another Sim Card there electrical and even the brand new ones can go bad i'v had mine installed in my 2 Maxx's for just over a Year & once i Installed them i have yet to Remove them. Knock on wood..
Give what i mention a thought and you might Try a System Cache Clear Followed by a Factory Reset doing one Won't hurt it any more than what it is already doing. Actually it might just help the phone..
Good Luck b33