I live in a house that was built in the early 1900s so the piping is really old and I didn't want to chance breaking anything so I went the cheap way out and I didn't sodder anything. I took the hose off from my hot water and added a T pipe that screws on to where the hose used to be. Left side sink right side dishwasher. Problem is.. the dishwasher works but the sink doesn't! Even when the dishwasher shutoff valve is off it doesn't work. I tried replacing the hose from the hotline to the sink and to no avail still no water :(.

What you have done is disturb mineral built up on your pipe walls and draw it up into your sink faucet where it's now clogging the valve.
First unscrew the aerator from the spout and check the screens. Turn the water on. If there's no flow then the inlet ports of the cartridge are clogged and the faucet must be opened up and the inlet ports cleared. To be more specific I will need the brand name of the faucet and it's age. Good luck, Tom