Yeah i agree with Tolak, tiger barbs are not recommended to be kept as tank mates with fish with long flowing fins, feelers, or are slow swimmers- this would include fish like angelfish, bettas, guppys, gourami's etc.
Tiger barbs are shoaling fish and do best in groups of at least 8-10 barbs, not just because they are shoaling fish, but also because when kept in larger groups they are less likely to fin nip other fish, but help keep the agression in their own shoal where they can handle each other a lot better. Personally i would recommend either;
a. Get the tiger barb a tank of his own which is at least a 3ft long 30gal tank in a shoal of at least 8-10 tiger barbs, with other fish which are carefully chosen to be the barbs tank mates, or
b. Rehome the fish to somewhere like a petshop or to someone who already has tiger barbs in a tank that has room for more and has a good fish stocking etc. You can try out the buy/sell/swap section on the forum if you like for rehoming the barb
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Ultimately keeping the anglefish in a breeding net is unadviseable, but keeping the tiger barb with the angelfish is also inadviseable because it is in tiger barbs nature to be active, shoaling and nippy fish, and you cannot change the barbs nature, so something must be done about the stocking of the tank to sort the situation out.
When you say "they give him carrots", do you mean this literally or something else?
To decide which fish is the most suitable for your tank and this which one (or both) need to be rehomed, what are the dimensions (length, width, height) of the tank and what fish do you have in it as well as how many and their sizes?
What is your average tank cleaning regime like (water changes, clean substrate and filter) and how often do you do it as well as how do you go about it exactly?
The angelfishes fins will help up if you use StressCoat dechlorinator and Melafix (to help prevent secondary infections setting into the wounds) and do lots of small regular water changes with dechlorinator (very clean water will help encourage the healing process), but the anglefish is unlikely to heal very well or quickly as it is as it will be quite stressed being in a breeding net, so sorting out the stocking of the tank is vital so it can go back into the main tank to heal in a less stressful environment
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