How long does it take to become addicted to pain pills?

Anonymous
I'm asking this because I've been taking Tylenol and Ibuprofen for several months, and I recently started taking Mobic and Flexeril. I take them for tension headaches and chest pain, but my doctor won't let me try alternative solutions for pain.

Honestly, I feel like a drug addict, taking medicine every time I have pain. Really, is that supposed to be the solution to everything? This is what I said to my doctor:

"I have a headache and I don't want to take anymore pain medicine." (Me)
"You can take Tylenol and Ibuprofen safely up to three times a day." (My doctor)

I had an ulcer from taking too much Ibuprofen, and I do NOT want this to happen again.
How long does it take to become addicted to pain pills?
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