Court wont let me serve tickets,Is this legal?

I have tried to serve tickets twice in a incorporated city within my city. I was turned away twice and the fines increased as well as incurring extra court costs. I was then arrested recently and turned over to this little city and was NOT given TIME SERVED. When I called about this I was told TOO BAD !! We arent going to remove any tickets from the Omni Computer and wont until YOU PAY THE TICKETS!!! Is this legal????? Houston Texas