Aggression Or Flirtation?

[RandomWiktor]

I have two 2 y.o (~ 7 in) common goldfish in my 75g tank. I've noticed over the past few weeks that their interactions have become seemingly agressive; the smaller of the two especially will ruthlessly chase the larger, usually head-butting his/her flanks and underbelly. Sometimes they'll both circle, nipping at each other, and it can go on for as long as 15 minutes. One even hurt his/her fin on the cave trying to get away.
However, I am aware that goldfish will also chase during mating season. I do not know the sexes of my fish (tried, but couldn't really tell), so I'm sure it is possible that I have a male and a female, esp. since one is so much larger when they're both the same age. I haven't seen any eggs though, so is it possible that I have two same-gender fish and they are fighting out of some kind of frustration or territoriality? The fighting gets especially bad right after feeding.
Any advice on what could be causing this would be great.

edit: Tangaloor, the smaller of the two who is picking all of the fights, is starting to get breeding tubricles, so I guess that explains it. So, now my question is: how do you find and destroy eggs, because I do NOT have the space, time, or money for babies, and I refuse to sell feeders.

 

[tjp]

its around that time for mating , the fish try to bash the eggs out o f the females and sometimes end up basing them to death! and males do times chase males . they get a bit conzused, and i shouldnt think its to do with filtration

 

[black angel]

There will be a big mess in the tank so you will know if theres any eggs,the water may go milky with milt and the fish will probably eat the eggs anyway. They look like little bits of sand stuck to plants. If you dont have any type of weed in there i suggest getting something like a few bunches of elodea so the female *if it is female* can be chased there and release any eggs.
If the chased fish head stands then its exhausted and should be seperated to recover.