I'll echo what some others are saying. I messed around with a seemingly minor achilles problem for too long, and it cost me 6+ months of training.
None of this advice will be satisfying or original. Sorry. But there's a reason you've heard this all before: It's true. I’m injured now (not Achilles), so here’s my advice to both you and to myself:
Take time off, now
Not to incite panic here, but you need to nip this in the bud. Take *at least* another week off, probably two. Maybe you don't need that much time off, but it's a big gamble to assume you don't. I'm not the only one with a terrible Achilles experience (and plenty of people have true horror stories). And seriously, two weeks is not a big deal in the scheme of things. You can cross-train (see below).
Do eccentric heel drops + foam rolling
Eccentric heel drops are the only thing that are going to make this work. Commit to them, and they’ll really help you recover and prevent recurrence of the problem. Also, tight calves put stress on the Achilles. Do *not* stretch your calves until your Achilles is healed, though, because that strains the tendon itself. Instead, get a foam roller and hit your calves hard. This might hurt at first.
Address underlying issues
Weak hip flexors and other stabilizing muscles are often at the root of injuries in the lower legs. Look up a routine to address these issues. Clamshells and variations thereof are your bread & butter here. This seems to have helped me, at least, to put this injury behind me.
Cross train carefully
I’ve been injured enough to know: Taking time off from running doesn’t have to mean time off from training. You just have to avoid anything that puts strain on the injury. Biking and elliptical machines can stress your Achilles. Some people say it’s fine for them, but just be careful. Deep-water running seems to give me the best possible workout with the least possible stress. It’s particularly good for emulating interval workouts and tempo workouts, and it builds leg strength in a hurry.
Return to running with caution
After months of starts and stops with an Achilles injury last year, I took a month off and re-zeroed my mileage to 15 mpw. I took a couple months to get back up to 50 mpw, where I was when I got injured. Don't let this happen to you - your comeback doesn’t have to be that slow if you take time off now. But when you start running again, I’d do only easy runs for a few weeks, and take a couple weeks to get back to your current mileage.
Accept reality, and don’t get discouraged
I have an existential crisis when I have to take a couple weeks off, but that’s kind of dumb. Hitting the pool and the gym hard for two weeks will reduce any fitness loss to about zero. Sure, you could be training harder if you were healthy, but you’re not. Sorry.
Just remember that if you address this now, you’ll be fitter in one or two months than you are today. If you don’t address this now, you run a serious risk of being less fit in six months than you are today. Good luck.