Let's assume that your peers cannot assign you a task that will take 6 months of exclusive work while you ignore everything else you are currently supposed to do. It seems like it would be useful for you to "bucket" these "look into" tasks as one of:
- half an hour to an hour to see if such a thing is even remotely possible. You're going to do like 3 googles and maybe a search on SO. You know now whether there is time for it today. If there is, say "I'll get to it after this, and talk to you in an hour or two ok?" Fully booked? Can you do it tomorrow? Tell them "some time this week" or "by the end of tomorrow" and then stick to that.
- half a day to a day. You're going to maybe try installing and running something, or using something, or watch a tutorial and then try it yourself. Presumably your peers can come to you for this because you have that kind of room in your schedule, but you may not have it today or even this week. Think a minute about when you will, and then tell them "in the next week or two unless you can get [whoever] to accept a one-day slip on [your current top priority] in which case I could do it tomorrow."
- days and days, no idea, it could be weeks or months. You need a week just to make the plan, and you won't know how long the pieces of the plan are for another few weeks after that. This should be a project with a plan and with internal deadlines and milestones. Your peers shouldn't be asking you to take on so much. Wait, rewind, what if they aren't? What if they just want you to do something smaller like see if it's even feasible or try one tutorial to see if it's worth spending the weeks or months? Yeah, that must be it, so rephrase the request to something you can fit in one of the previous two buckets, give the corresponding answer, and then add "after which we could start making a plan for the whole sort of project to actually implement that for real. That's probably several months' work."
You can also timebox the work. That is, if they need it Friday, you'll only be able to put in 4 hours on it. Will that be useful? Ask them.
Two very important skills for any worker are to guess (with some accuracy) how much work something is and to manage their outstanding tasks. Your peers are asking you to do this and expressing disappointment that you can't. Now would be a good time to get better at this. At first you'll literally just be making things up. That's fine. Say you think it's 3 googles and so you say "in an hour" and 90 minutes later you're down a rabbit hole completely lost and your coworker is at your desk asking for your conclusion. LEARN. Next time either don't underestimate it or don't get dragged into details or don't start installing things when what you planned was a quick google. You will get better with practice.
Another way many people improve is with rather obsessive note taking. How long did you think a thing would take, how long did it take, what was the long part? (Eg 3 Googles took 3 minutes but drawing the diagram to explain what you learned took 2 hours.) At any moment, do you know all the promises you have outstanding and when they're due? Are you able to see whether your rough guesses are any good or not? Get better at both guessing and at meeting your guess (by stopping when time is up) as time goes by.