thank you for the questions. 2 months would have been more than sufficient time for a superficial abscess to heal by secondary intention.
As Dr Ang has mentioned, the pictures do look like the abscess has healed. All the purplish tissue you mention are usually the scar tissue that has resulted from secondary healing. They usually become softer over time. The sensitivity also gets better with time.
If it is very sensitive, sometimes it is due to the nerves being over-sensitive, and a desensitization program done by a physiotherapist may be useful. An alternative is also to apply some scar cream like Dermatix.
Assuming it is just an abscess and nothing else, your bones and muscles should be ok. So I don’t see any problem in you getting back to exercise. Perhaps start out with brisk walking? You can slowly progress from there as you get better and stronger.
Hope this helps,
Dr Sean Ng