Finally I solve the problem, I tried all your recommendations and finally I nailed it. THANKS TO ALL FOR YOUR HELP!
Well so first of all, I remake my whole circuit, making it cleaner.
I know, I know, it's still messy but I did my best. For my luck the problem still there in the LCD. So I followed dc42 advice and connect my LCD directly to my arduino, and it didnt work either, but with the snubber parallel to the load and the LCD connected directly to my arduino the impossible became possible
, now it´s working and the display works great.
So this is my snubber (Resistor 100 ohms 1W, Polyester capacitor 250V .1uF:
In my local store the ceramic capacitors are only of 50V so I tried with a polyester one (250V .1uF) and a resistor of 100 ohms, 1 Watt because of 1/4 watt it burned.
So my solution was adding the snubber in parallel to the Water pump and connecting the LCD directly to the pins of the arduino 5V and GND.
Thanks again for all your help.