If you can get to a gym you can keep your cardiovascular fitness topped up by cycling and rowing. Also core fitness exercises. All this will help keep you focused on your target and keep your body strong and accustomed to tiring exercise. Not as much fun as running for many people but when you do get on the road again you will not be starting from scratch.
By the way your body starts to repair itself immediately when injured. You injury may not be as severe as some or may respond well to treatment. Arguably a 10/11 minute miler should do less damage than a 7 minute miler. Are your training shoes O.K. not rubbing your achilles? Be positive all runners' get injuries.
Rather than take anti-inflammatory tablets I would suggest using a gel (before icing for 10 minutes) directly on the injury but only so long as you have any pain or swelling.
Re above exercises, normal walking in proper shoes will give your injury natural exercise and physiotherapy at the outset. Some may suggest that wearing a higher heel shoe will ease any pain and it will because your achilles will not be stretched but the downside is that it may heal shortened and risk another injury.
You know you must rest for a few weeks. Very frustrating but if you don't it will become a walking problem not just running. Achilles is potentially a longer term injury more so if not treated correctly.
You need R.I.C.E. Rest, Ice, Compression and Elevation. I would exclude the "C" as it is a difficult area though any swelling should reduce with R / I /E. Do this often each day but ice should not go directly on skin (wrap in towel or go to Boots for icepack) Don't wear anything that could be described as 'high heels' sensible shoes with a big flat heel are ideal. Definitely not flatties or pumps! If you have a nurse at work have a word.
Finally if you have a good, sympathetic G.P. make an appointment. Otherwise see a local physio. If you need a recommendation ask a local sports club who they use. You will be lucky to get seen for less than £30. Your first visit should be about an hour because there will be a chat to find out about your general health, running and any medicines before treatment. Subsequent visits will probably be half an hour.
The physio, in addition to treatment should advise you about exercises and possibly tell you how the injury came about i.e. sudden increase in mileage / you may have ignored a niggling ache until it was too late.
A couple of girlfriends (sisters) were out having a meal and the restaurant was not very busy. In came Billy Connolly who sat down and ordered. They could not help furtively glancing at Billy from under their long hair and Billy was aware enough of them to furtively glance back at them from under his long hair so much so that they all started laughing. He came over and joined them they had a great time. He paid their bill before leaving.