You have a daughter together and it is vital that you maintain a dialogue with your ex. You should also assume your share of the childcare responsibilities. It's a positive sign that your ex is sending you photos of your daughter so that you are still actively involved in her life.
What I'm a little concerned about, is you "doing stuff around the house." If it's for your daughter's benefit, then all well and good. If it's not, then you need to consider saying no. Your ex cannot cherry-pick which parts of you she wants and doesn't want. Keep yourself busy and don't rush around there at a drop of a hat unless, of course, your daughter's welfare is at stake.