When ever I flush my toilet in my bedroom there is a girgling noise heard through the shower drain,this started happening about 2 months ago.I tried drain cleaner in toilet and shower but didn't make any better at all,I think I have a plumbing vent problem.

I think I have a plumbing vent problem. And I'm sure you have one!
The sound you hear is the toilet attempting to vent through the shower trap. The solution would be to snake the lavatory roof vent. Put out enough snake to reach the base and 16 feet more. Good luck. Tom