Both head ligth and tail ligth is out on the left side of the car I think it is a fuse but which one.

Tail lights are on a different fuse than the headlights. If you already checked the bulbs then check the fuses. They're under the dash, on the left side of the driver.
Hope this helps.

just check accurately bulbs if you mixed it could happen like that, some cars for the brake lights use two contact bulbs some of them single contact, two contact bulbs can give two signals which one is used for brake ligths and another for taillight, so check the bulbs carefully

fuse block under dash on left side of car

I think the trailer wiring is incorrect.

If it happened the way you described it. I don't see how it could possibly have damaged anything. I guess what you are saying is that the left tail lights are not working? ("4 way exterior dim lights"???) Touching the tail light wire to the turn signal wire will only cause your turn signals to light up. (I am assuming that the tail light switch was on at the time)
I think it is more likely that the brown wire touched ground. This would make a bright flash, blow a fuse and cause the symptom you are describing...I think you need to check the fuse again.
There are separate fuses for the left and right sides. The left side tail lamp fuse is fuse #7 in the junction block it is a 10 Amp fuse. The junction block is located on the right cowl side inner panel - We are NOT talking about the Power Distribution Center under the hood.

All of the above is also assuming that we are talking about a plain Cherokee, Cherokee SE, Cherokee classic or Cherokee Limited.

If we are talking about any of the Grand Cherokees, you may have a fried lamp outage module.

check taillamp fuse in fuse block...probably blown.may have short cause fuse to blow.these can be difficult to find.

Do you have trailer hitch with trailer wiring? Also check tail light housings for water intrusion.

fuse to check should be brake -running -ligths but i think they run off the same fuse . or look for tail lps fuse in panel

try to replace the bulb it can be also short,

Check the fuse in the fusebox inside for a blown fuse,the brake lights are working so check the plug going onto the back of the lamp for tightness,could be a loose connection.