Should I Get Some Brand New Tires For My Car?

I just bought some used tires last month. I replaced all four because they were all worn down. I don't have much money so i bought some used tires at a used tire shop. I can't afford the ones from the store for $60 each plus installation I got these tires for $20 each. The type of tires i got were kind of smooth. Maybe too smooth. They other day i stepped on the gas and the tires kind of skidded a little bit. And yesterday it was raining and it was slippery and i could feel the car kind of skidding a little bit. It's not much but i could feel it a little bit. And i wanted to know if i slammed on the brake if the car would stop before the stop sign. Nope. I was barely going about 35 mph and slammed on the brake and i passed the stop sign by like 12 feet. I think i need more rugged type of tire. DO I NEED TO REPLACE THEM REAL BAD?