Can I get chlamydia pinkeye again from using old / expired eye drops?

Don't use old drops. You can contaminate a bottle of eye drops by touching the eye, but the drops inside have preservative to protect them, and the bacteria on the outside probably die by drying out. Multi-dose bottles have preservatives; single use vials do not. In a fridge, the longest you should probably keep the drops is 30 days, once opened. Link: http://drkisling.Com/2011/09/19/how-long-can-you-use-eye-drops/.