A Schrader valve coming loose is a rare occurrence. If you didn't damage anything and the valve core itself is coming loose, there's a tool to tighten them. Old-fashioned valve caps actually had this tool built in. You can still buy the tools for a couple bucks at auto parts stores. But of course, a new tube will cost about $3 and solve the problem.
The tyre should be fine, the problem is with the inner bike tube. It is useful to know what type of valve your bike tube uses. Schrader valves have a middle pin surrounded by an outer ring. Presta valves have a movable nut that allows you to inflate or deflate the tube. It sounds like your bike tube has a presta valve you have damaged the movable nut by loosening it a bit too much and/or being a bit too rough with it when using the bike pump. Unfortunately, it can't be fixed. If that is the case, you will need to buy a new bike tube (and keep a spare one handy as well) edit - That's weird, Schrader valves don't usually do that. It must have been an old tube or a faulty one. You'll be needing a new bike tube. edit - Well, I didn't know you could fix them, but still it'll be less hassle if you just brought another tube.
It sounds as if you just need a new inner tube if there is a valve problem. New tubes cost only a couple of ??? each, and it's worth getting a couple of spares and a puncture repair kit if you don't have one. If you have some mates who also cycle, it can be worth getting a box of inners and splitting the cost. That way you get the discount and some spares. Check that you get the right size for your tyres.
