You could consider Access forms, and then have the tables reside on SharePoint.
You can then say base the form on a query, and in that query you could provide (have) the user name included as part of the query where clause (thus a user removing or changing the forms filter will only provide a view of their own data.). However, such uses if they fired up Access (or even Excel) could wind up with seeing all rows in the table and not what the Access query restricts the data to (the one user).
Unfortantly with Access desktop? And like most desktop software? Well the goal and design and history is that of allowing ease of data editing and viewing. So, just like when you walk into a bank, and wait in line? Well, when you get to the teller, they will fire up a access form based like system and pull up your account information. And any and all tellers can see/view and pull up that data because that is what the software supposed to do, and do well. (get at any customer data).
Now, flip this problem, and create a user web banking system, or even a instant teller. Now the problem is backwards. The software's goal is not ease of editing data in a table, but ONLY allowing the user to see THEIR data. So a very different kind of problem.
It is very (beyond very) to note that web development tools do not out of the blue or automatics restrict data to JUST the one user. It is YOU the developer that makes that choice. So, if we could press a button and have a access form converted to the web? Well, then that access form would do its job in life. That job is to allow you to edit all that data in a table. Not just YOUR data.
For example, have you ever written a Access application that JUST displays each users own data? I am betting not! It is hard to do. (because the roots of Access is ease of editing data). As noted, I cannot stress that web development tools do the SAME thing. They can let you edit data. The editing of data is thus a software issue and development issue. The data system or Access or even SQL server? They just hold data. It is YOUR software that has to decide that ONLY data for the one user is to be displayed.
Now so very often web systems ONLY show YOUR data. But that VERY common case is due to the nature of web systems, and that your not a bank teller, or a company employee, but that of a consumer of that system. And each consumer now is 100% opposite of what most software systems do naturally (that is get data from a table).
So, I can't stress this concept enough. That concept is that web software and systems do NOT make this restricting of data choice for you. It is your developer tools that MUST have this ability and ALSO the choice of how you build such systems.
Web systems can do this data restricting data better for several reasons.
One big reason? Well, most of the time you adopt some kind of security and logon system.
Thus, parts of the web site now are restricted based on your logon system. (hey, maybe you use Facebook logons). So web systems have a very good and wide and broad system of supporting some kind of logon system. For desktop software? not so much.
But EVEN with that very robust and type of security system and logon system?
You the developer STILL have to make the choice of what data they see. Maybe it is traveling salesmen on the road. And thus every user of that web system still has to be able to edit, view and add customers to that system. This common case is not really different then a typical Access form to edit data.
So only SOME types of web applications need that restricting of data to JUST the one logged on user. But, because web systems have that "better" logon system? Then you the developer can thus now use that logon to restrict data with greater ease then what desktop software dev tools often offer (say like access).
So, a lot of this will come down to the web tools used. If you pulling data with Excel, or Access? Then it considerable more difficult to pull JUST data that belongs to a given user. And your software will require designs from day one with these restrictions in mind.
Again, at the risk of repeating myself?
the tools don't' make the data restrictions for you. If you need secure data for ONLY the given user, then you simply have to adopt a set of developer tools that allow this concept in mind. And that tends to mean the tools you use do NOT by default allow users to directly edit or link to some big table of data that contains all users data.
This is also why say a program written in VB6, or now vb.net can be more secure then Access. (because those tools by default don't provide forms that are designed from day one to edit all rows of data). So, the UI does not present default forms and things that gives users the ability to edit all rows. As a result, then the software can now control what records the users sees, and since they don't' have some default form that allows viewing of all rows.
It thus becomes more practical to write software that only dishes out their own data. But again, and I can't stress this:
The choice of what data to display is a choice of the software developer - not the database nor the web development tools.
It thus stands to reason then you have to chose the appropriate tools that will allow you to write software that restricts the data in a manor you require.
General questions on SO in regards to what flavor of ice cream or what dev tools to use tends to be frowned upon, and is quite much against the general rules for solving software and code issues you have and post on SO.
But, if you come from say Access with VBA skills? Then I would suggest adopting the free verison of Visual Studio and go with vb.net + asp.net web forms. Web forms are close to end of life, but they are by far and away the best choice, the least effort (coming from Access) and will give you a robust security model in which you can restrict data on a per user basis.
I would not duck tape and try to cobble together such a system with office tools, since they are not really designed for that type of data restricting you need. So, go with some good quality web tools like Visual Studio (free version is fine) and use SQL server (free version again) is really the way to go here. If you need a truck in place of a car, then get the right kind of truck, and don't try and use a car for that transport of goods, or in this case build a secure web database system.