When can I get back to running with Achilles tendon problems?

Depends on severity. Many runners, especially those that are advanced, run with mild achilles tendonitis. More severe tendonitis or partial tears often need a prolonged period of rest (1-6 mos.) from running and aggravating activities. Most benefit from a customized footwear evaluation, physical therapy, and some require bracing or immobilization. A sports medicine physician can help guide you on a return to running.
Couple of things. You need to heel the achilles problem first and work wtih a physical therapist to get running again.