I have noticed this a great deal in IXFJs. It can be good in the sense that someone else’s positive mood can rub off on them… and bad, because I have sometimes seen the IXFJ start to hate something they loved, because a person close to them hated it, trashed it, and changed their mood about it.
(All feelers can suffer from this to a degree – especially if you rate high on the ‘affability’ scale, which means you have an overall pleasant approach to others.)
You have already won half the battle by realizing you do this, and wanting to change. Next you need to become aware of it as it is happening, and learn to detach enough to ask yourself, “Am I feeling this… or are they?” To realize you are a separate entity from this person, that you can choose whether or not to allow their emotions to influence yours (you have Si as a barrier to help you, which you can activate through asking detail-driven questions to understand their mood and perhaps force them to be objective in the process, pausing to examine your past interactions with this person, and maybe to recognize a pattern of behavior or a certain dynamic between you), and analyze things (Ti) as they happen, rather than allowing other’s moods to “overwhelm” you.
You can also shape the emotional mood around you, rather than being reactive – choose to be proactive, and if the mood is bleak, focus on how you can uplift that person (provided they are receptive and really do want help). The strength of Fe is understanding and shaping complex personal dynamics within the group – you are terrific at sensing / feeling them, now learn to USE them. Healthy Fe-doms are very good at shaping the mood of a group, by setting a strong and positive emotional standard. You can learn similar techniques.
Since you are an ISFJ, I’m guessing some people’s moods influence you more than others – your beloved family and close friends, maybe? The people you most care about? Typically, emotional detachment is higher with total strangers, those you do not like, or those you do not know well than those in whom you wholeheartedly invest your emotions. Being emotionally engaged with those people is not wrong or bad – they are “your tribe,” and it’s common to be emotionally influenced over those we most love or care about. This is where my advice to step back and think about (analyze) it will be harder. But unless you are reasonable about others, you cannot see them clearly.
The next time someone you care about goes into an emotional meltdown – give yourself some space, leave the room for a few minutes, go somewhere, shut the door, and work through your feelings / reach a point where you can analyze what just happened and whether it’s rational for you to be upset with them. In the case of “worry” … anxiety is an emotional response. How do you counter an emotional response? With logic that “comforts.” If it’s a problem, what are the ways you can solve it? Fix it? Lay out steps to help the other person be proactive?
The human mind does not like uncertainty or indecision. Until you make a choice, you are “stuck” in limbo. You cannot make these six decisions, until you make THAT decision. Decisions build on one another. You can combat anxiety – your own and other people’s (if they will listen) through decisions. A leads to B, which makes C inevitable. Suddenly it’s not so scary anymore, because you have a plan. You may deviate from the plan, but your mind can calm down for awhile. :)