Tonight she is going out with her boyfriend and fucking him.
That's entirely proper, of course.
Yesterday she gave me her dirty panties to wash, which I am doing now while she is out with him.
Good for you. If your woman told you to wash her panties and you obeyed her, you did the right thing. Are the two of you living together now, or do you have a key to her apartment so you can go to her place to carry out such tasks....?
I also went out to a store tonight to buy her new panties.
Excellent. Your woman needs sexy lingerie, of course, so she can turn on her lover.
Before she went out she made me send her a video of me stroking my cock. I am not allowed to cum until I see her.
Perhaps she is seeking reassurance that she continues to turn you on, by making you show her in a video that you are fondling you cock for her (but not allowing you to cum). But, this is confusing. How can you fondle your cock if you are wearing a chastity device and she is your key holder....?
She also told me I had to clean my floors and my bathrooms....
If your woman feels your floors and bathroom(s) are not adequately clean, then cleaning them for her was the appropriate thing to do.
.....without wearing my “panties.”
"Panties?" You haven't mentioned that your woman keeps you in panties. But, as her cuckold (in essence.... given that you aren't married), it would be appropriate for her to keep you pantied. You might suggest she take you to a women's lingerie store, select several pair (pink, perhaps) of feminine panties that appeal to her, then stand behind you while you wait in line at the cash register, then give you cash to pay for them when your turn comes up, then have you turn and give her the change. Then, she could repeat this exercise with you until you have an entire week's worth of feminine panties to wear every day (over your chastity device), so you can throw out your tightie-whities or whatever you normally wear.
She also told me next time I need to come over before (earlier?), so she can put me in my cage and so I can wash her before she goes to fuck him.
Clearly your woman has you on the right track. You might remind he, though, that your cock cage belongs on your cock, not at her place, with the key on a chain necklace-like around her neck (which, you might point out, will turn on her lover even further).
She said I might get to clean her pussy in the am.
That's something your woman should require of you — preferably with her queening you; i.e., with you on your back (in the nude, wearing your cock cage), with her straddling and riding your face while you suck and lick her cunt with your tongue and lips, hopefully bringing her to another orgasm.
She also told me that I can’t hold back cumming when I fuck her next time so I can be her little bitch.
It's totally appropriate for your woman to view you as "her little bitch." Perhaps it will help her to do so if she makes it a point to always fuck you on top (with your cock cage off, temporarily, and your feminine panties pulled down to your thighs), so she can move in ways that are most pleasurable for her.
It sounds like you're doing well as your woman's appropriately-submissive cuckold-boyfriend. I encourage you to keep up your good work.