I don't know if you care about being legal, but a B20 block in an integra will NOT be legal from a visual smog inspection standpoint.
To try to answer some of your questions... Metal shavings will not likely be a headgasket. Most likely it's bits and pieces of main or rod bearings, because you said you heard a loud knocking. I doubt you put a hole in anything, but I guess anything is possible. A new or rebuilt bottom end is definitely on order.
You say you'll most likely be paying for this with school loans. Not the best idea, but, if it's all you have, then I guess that's the only way. Plus, they are low interest, so it's not as bad as putting it on a credit card.
My opinion. for what it's worth.
Get a Helms manual for your car. It's good to know what you are doing, and to have a book that knows when you do not.
Get a b18b block, out of a 94-99 integra ls. 96+ is preferable if you can get one for a decent price, as the obd2 oil pumps are all the same across the ls/gsr/type r trim level, so you'll have the advantage of having a good oil pump compared with earlier generation b18's.
Next - pull the pistons/rods out of the new block and get ARP rod bolts installed on the rods. Make sure the machine shop resized the big end so it is perfectly round.
Next - make sure the rod and main journal bearing clearances are good using plastigage. If needed, change out the bearings to bring them to spec.
Get the block honed per the specifications in the Helms manual. Install new OEM Honda rings on the pistons.
This will give you a nice cheap block capable of 300whp. I don't anticipate you spending more than $1k on the bottom end, including the purchase of it, if you buy wisely, and do a little searching around.
You can keep the head that is in your car, provided that it is still in good shape. A DIY turbo kit and engine management will set you back around another $1500, but you can run the stock head and head parts and stock everything until you want to spend the cash on a turbo kit, because it will be a basically stock engine.
Spend the money to get a shorter geared transmission. The ls transmission sucks, the end.