Penicillin is an intermuscular injection and you do NOT want any blood in the syringe, you only want that if you are trying to give an injection in a vein, but the others are RIGHT!!! Who told you to give penicillin for this injury? It makes no sense to me either, and unless you have clear instructions from your Veterinarian, STOP NOW.
Please get a vet to look at this, it sounds like youve gotten some very bad advice so far. You probably do want to run cold water over the swollen area esp if there is heat in it, and afterwards, you may want to wrap the lower part of the leg NOT THE area that was kicked though!!! This is so as to reduce swelling below the injured area because excessive swelling can cause some damage of the joint capsul etc of the fetlock, but ONLY IF you know how to put on leg wraps properly. If you have any doubts about that do not wrap, because done wrong it can do more harm than good.
//edit// ok, I just re-read your OP and if it had reduced already but blew up again after more stress, I'd just hose it with cold water, run a hose over it for 15-20 min, dry it off, let it rest a while, (few hours) check it again, if it is hot and swollen again, re-hose if you can, repeat. repeat. repeat.
You can hose it a few times a day for probably several days, and that will probably do as much good as anything. Unless there is some kind of open wound that is clearly infected, why on earth would you give penicillin? No No NO NO. Keep the horse in a stall where he can be comfortable but not move too much, and will not be able to attempt any more jumps, and let it get some rest. Walk him/her gently as he/she improves and the swelling reduces and do not ride or let him get a lot of exercise untill there is no heat in the joint and the swelling stays down after walking. Then, keep checking so you see if the swelling starts to come back. If it does, go back to just walking on a lead, no riding or pasture exercise.
At least talk to a vet and see what he recommends for swelling, (bute (Phenylbutazone) may be useful but don't overdo with it. In excessive quantities it is bad, hard on kidneys and liver, but for a specific period of time, is useful to reduce swelling and to keep comfortable... do not use it for more than a couple weeks it also masks pain too much and pain can be a good guage to injuries)