Weight lifting makes you slow?

Ok, another question. I am around 5'6'' (168cm) and weight 127.9 lbs (58 kg) and as a light person one of my best ability is my speed. But i do lack some power. Of course i do push ups and pull ups during training, but people tell me to do some weight training if i want to gain more power. But some say that you will lose some speed in return for some power when weight lifting. I want to know wether this is confirmed, or is it not true. Can i maintain my speed while gaining more power. I read on the internet you will lose speed when weight lifting if you work out after a certain minimum weight. But then again some say, no matter what weights you train with, you will lose speed. Now i dont really want to lose my speed as its the only thing im kinda talented at. But i do want to scare my opponents because no matter my how many times i hit em, even with sharp counters, they rather fight me then a very powerful one. This is a real dilemma for me, because even my coach tells me i need to stomp sum fear into my opponents. So does weight lifting really makes me slower, or can i just buy a pair of dumbbells? As always, thanks in advance