I have a problem with sewer backup in the basement when there is a heavy downpour. A waterproofing company installed pvc pipes in the basement and a pump but that only takes care of ground water if any, that comes in the basement. I paid $4500 for that job which I see now was a waste. The main problem is preventing the sewer backup from coming in. I spoke with a plumber who wants to knock down my walls but I don't want to do anything until I am sure that this problem can be resolved and how it can be resolved. He said something about a sewer trap could be open. How do you prevent sewer water from coming in if the house is in a low lying area?

If your city sewer backs up during a rain the problem may actually belong to the city. Call the city sewer and water dept and ask them to check the main out by the street. In my town they recently found many illegal sump pumps draining into the city sewer and that was a cause of backups on my block. The $4500 you paid was for a perimeter drain and sump pump that should drain outside into your yard. It would not cause/solve the issue you described.

If you have sewer backups during heavy rains it is usually excessive water from roof leaders sump pump and weeping tiles surcharging the city main.
If it was you own line surcharging, the sump pump should take care of that problem.
The next step is to install a backwater valve. This will prevent sewage from the city main backing up into your basement.

I will attach the link to the best backwater valve that I have found to date.
<www.backwater-valves.com>
Check with the City to see if they have a subsidy program, I am involved with starting the program in my area. If enough people install sump pumps and disconnect weeping tiles it saves the City a lot of money in treatment costs and damage from backups.
Hope it helps

p.s. You didn't waste your money doing the work you have done as the backwater valve has to be installed in conjunction with a sump pump in most cases.