That cage is too small, yeah. Generally the minimum for one lovebird is to have the smallest side be 18 inches or about 45 centimeters but since they are such active birds I think 21 inches or 53 centimeters is a more humane minimum. It's hard to tell from the pictures but that almost looks like it could be 12 or 15 in wide (30-38 cm) so pretty small.
They are probably fighting for territory and with lovebirds this can end in a dead bird. I'm not trying to scare you, but they have started fighting and this is the reality you face now. You need to get them separated as soon as you can! One of them could really get hurt or maimed if they get more serious.
Even if it means buying another small cage just so you can keep them apart while you get the money for two new larger cages. Keep an eye on them too, they could have injuries that need vet care from that last fight.
Be aware they will also bite at toes through the bars also.
The good news is, that cage is probably the source of some of your problems right now (their aggression towards you and each other) so two larger cages will probably help
a lot in time. They might even be able to be together again in a very big cage given time to forgive each other but I would definitely wait on that, they really need personal space right now if they are drawing blood.
Baby birds don't mind being crowded and don't demand space but adult lovebirds will claim and defend their territory with violence if necessary.
If you'd like I can try to offer advice on better cages? Though I don't know which country you are in and my suggestions would really only apply to people in Canada and the USA (though maybe it could give someone ideas too?)
Now even if you do get bigger cages it might still take time for them to settle down again and effort to become tame outside the cages but I hope you stick around Avian Avenue, @
fluffypoptarts probably has better taming advice than I do for multiple lovebirds.
I hope your little one is okay, poor Shelby. Do you know their genders?