1. IT IS OKAY TO ASK FOR HELP
If you look like you are holding it together all the time, people may not realise you need help. Learn to delegate and appreciate other people's help, even if they don't do it to your standard.
2. SAY "NO", WITH REASONS
To avoid offending people, explain why you can't do that task right now. Also offer reasonable alternatives. For example, sometimes, "no" may mean you put the task off for a while, or you agree to do just one part of it.
3. PROPOSE FLEXIBLE WORK
If you must focus on something outside of work now (like a sick child), explain how you will continue to deliver results, and how work will be spread around the rest of the team without harming business. Suggest a trial period and ensure you prove yourself!